There are 18 compound verb forms in Esperanto, 9 in active voice and 9 in passive voice.  I will first make a general statement about the meaning of these compound forms and then give examples.  If you do not at first understand the principle, do not despair;  the examples will clarify the matter.  Since the Esperanto system is very similar to the English system, my first examples will be from English. 

Suppose that I make a statement at a certain moment in time, let's say t1, using a compound verb.  That statement indicates my attitude or mental state at another time t2 about some action.  Thus two things are involved: 1) the action itself and 2) the way that I view that action.   Obviously the action itself must precede t2.

Suppose I say, "I am washing the car."  The action is washing the car, and my involvement with it is hands-on, participatory.  I am at this moment participating in the action.  If I say, "I have washed the car.", the action is the same, but my relationship to it has changed.  I am now focusing on the result of the action, the fact that the car is now clean as a result of my having washed it at some time in the past.  If I say, "I am going to wash the car." the action is again the same, but now my attitude toward it is different.  My mental state is now one of anticipation;  I am focusing on what I will (probably) do in the future.

The term 'tense' is used to describe the relationship of time t1 and time t2.  In the above examples, t1 = t2, that is, the time of the utterance is the same as the time of my mental state, i.e., the same as the time when I am thinking about the action.  These examples are in present tense.  The term 'aspect' is used to describe the way I see or regard the action.  If the action is in the future relative to the time when I am thinking about it, my attitude is some of anticipation.  If the action is in the past relative to the time when I am thinking about it, I am focusing on the result.  And if the action is occurring at the same time that I think about it, I am focusing on the action itself.  Let's say that my attitude is one of participation.

The 3 aspects, participation, anticipation, and result that I have described in English exist also in Esperanto and are indicated by the second part of the compound verb form, which is called a participle.  The first part of the compound form is some form of the familiar verb 'esti' = 'to be' and indicates the temporal relationship of the utterance to the mental state being described.  In all of the above examples, we used the present tense form 'estas'.  The participle is a verbal root with a special ending. 

The present participle indicating participation ends in '-anta'; the past participle indicating result ends in '-inta'; and the future participle indicating anticipation ends in '-onta'.

Mi estas lavanta la aŭton. = I am washing the car.
Mi estas lavinta la aŭton. = I have washed the car.
Mi estas lavonta la aŭton. = I am going to wash the car.

Note that all of the above participle end in '-a'.  They function as adjectives which describe the subject 'Mi'.  But they also have a verbal character which allows them to take a direct object, in this case 'aŭton'.

Now suppose that instead of making an utterance about by present mental state, I want to describe my mental state at some time in the past.  That is, t1 follows t2.  There are 3 possibilities for my mental state as before and the participles that I use to describe it are exactly the same as before.  But I will now use the past tense of 'esti', namely, 'estis' to indicates that I am speaking about my mental condition at some moment in the past.

Mi estis lavanta la aŭton. = I was washing the car.
Mi estis lavinta la aŭton. = I had washed the car.
Mi estis lavonta la aŭton. = I was going to wash the car.

Finally suppose that I want to describe my relationship to the action of car washing at some moment in the future.  That is, t1 precedes t2.  As before there are 3 aspects: participation, anticipation, and result, and the participles are the same.  I now use the future tense form of 'esti', namely, 'estos'.

Mi estos lavanta la aŭton. = I will be washing the car.
Mi estos lavinta la aŭton. = I will have washed the car.
Mi estos lavonta la aŭton. = I will be going to wash the car.

These compound forms allow the speaker to be very precise about the temporal relationship between the time of the utterance and the time of the mental state being described and about the nature of that mental state.  Generally such a degree of precision is neither necessary nor desired, and the use of these compound verb forms is much less common than in English.  So for "I am doing the exercises at the end of the lesson." one would ordinarily say "Mi faras la ekzercojn ĉe la fino de la leciono." although "Mi estas faranta . . ." is possible, and for "I have sent them to my teacher." one would ordinarily say, "Mi (jam) sendis ilin al mia instruisto." although "Mi estas sendinta ilin . . ." is possible.  Correspondingly at this point in the learning process, being able to determine the meaning of compound forms when you encounter them is more important than being able to use them.

All of the above examples have been in active voice.  Exactly the same principles apply to passive voice.  The participle endings are '-ata', '-ita', and '-ota'.

La aŭto estas lavata. = The car is being washed.
La aŭto estas lavita. = The car has been washed.
La aŭto estas lavota. = The car is going to be washed.

La aŭto estis lavata. = The car was being washed.
La aŭto estis lavita. = The car had been washed.
La aŭto estis lavota. = The car was going to be washed.

La aŭto estos lavata. = The car will be being washed.
La aŭto estos lavita. = The car will have been washed.
La aŭto estos lavota. = The car will be going to be washed.

For completeness we may as well say that it is possible to combine the US-form of 'esti', namely, 'estus' with these same participles.  Such forms are not very common.  Likewise 'esti' itself can be combined with them to get compound infinitives.

So far we have treated the combination of some form of 'esti' with a participle as a compound verb form.  It would also be possible to say that the only verb involved is 'esti' and that the participle is a predicate adjective which modifies the subject and indicates his mental state relative to some action.  Correspondingly the participle carries the adjectival ending '-a' and agrees in number with the subject.  So in "Mi estas leginta tiun libron.", 'leginta' is a predicate adjective which describes the subject 'mi' and says that the subject is characterized by the fact that he has read that book.  Maybe it would be better to say that 'leginta tiun libron' is a participial phrase which funtions as a predicate adjective.  Participles can also be used as attributive adjectives (i.e., adjectives that aren't predicate adjectives).  So

La viro staranta apud la arbo estas mia onklo. = The man standing beside the tree is my uncle.

Tiu legota libro estas interesa. = That book, which is to be read, is interesting.

Kie estas la jam riparitaj iloj?  Ĉu iu apartigis ilin de la riparotaj?  La riparataj estas en la apuda ĉambro. = Where are the already repaired tools?  Did someone separate them from the ones to be repaired?  The ones being repaired are in the adjoining room.

La ŝtelisto estas tiu viro portanta la verdan kravaton. = The professional thief is that man wearing the green tie.

If we change the participle ending to '-o', we get a noun characterized by the action of the verbal root.

La lernantoj en ĉi tiu lernejo estas malriĉaj. = The students in this school are poor.

Oni ne povis rekapti la fuĝintojn. = It was not possible to recapture the fugitives (those that had fled).

Tiuj punotoj ŝajnas malfeliĉaj. = Those (people) who are to be punished seem unhappy.

There are some limitations on the use of participles ending in '-o'.  A limitation on participles ending in '-e' is that they can only refer to the subject of a clause.  They provide more information about the subject in addition to that provided by the main verb.

Enironte la klasĉambron, la nova instruisto inspiris profunde. = About to enter the classroom, the new teacher took a deep breath.

Malferminte la libron, mi surpriziĝis multe, trovante bileton de 20  dolaroj. = Having opened the book, I was very surprised, finding a 20 dollar bill.

The suffix -ado

The precise meaning of this suffix depends on the proper sense of the root.  Consider 'broso' = brush (instrument for brushing hair).  The root is substantive, and the derived verb is 'brosi' = to brush.  If we want to form a verbal noun which indicates the action of brushing, we cannot simply change '-i' to '-o' because 'broso'  is already taken, as it were.  It designates the instrument or tool used for brushing.  To get the verbal noun, we add the suffix '-ado', and the result is 'brosado'.

Now consider 'kombi' = to comb.  The instrument is 'kombilo' and we can, and do, use 'kombo' to mean the act of combing.  It is not necessary to add the suffix '-ado'.  We can, however, add it to get 'kombado' if we wish to indicate that the action was on-going, that it went on for some extended period of time.  Likewise the verb 'kombadi' indicates a repeated action that goes on for some period of time.  So 'kombo' is the verbal noun corresponding to 'kombi' and 'kombado' is the verbal noun corresponding to 'kombadi'.  In my view the dividing line between the forms with '-ad-' and those without it is rather fuzzy and not sharply defined.

More about -iĝi and -igi

In Lesson 14 we said there were two more important cases involving '-iĝi' and '-igi' to be analyzed:  1) the root is a transitive verb, and 2) the root is a non-stative intransitive verb, like 'morti' = to die.

Stative verbs

Before we consider these cases, it is worthwhile to point out that in the case of the stative verbs that we considered in Lesson 14, like 'sidi' = to sit, the forms ending in -iĝi  and in -igi always involve an understood participle ending in -anta or -inta.  Note that in additon to the suffix '-iĝi', there is a self-standing verb 'iĝi' which means 'to become' and in addition to the suffix '-igi' there is a self-standing verb 'igi' which means 'to make'.

   La infanoj stariĝos (iĝos starantaj). = The children will stand up (will become standing).
   La vizitantoj sidiĝis (iĝis sidantaj). = The visitors sat down (became sitting).

   La teroristoj kuŝigis la ostaĝojn sur la planko (igis ilin kuŝantaj). = The terrorists made the hostages lie on the floor (caused them to be lying).
   Flugigu kajton (Igu ĝin fluganta). = Fly a kite (cause it to be flying).
   Pendigu la kanajlon (Igu lin pendanta). = Hang the bastard (make him hanging). 

Consider the transitive verb 'refarbi' = to repaint.  "Mia patro refarbis la domon lastan monaton." = "My father repainted the house last month."  The house underwent a change of state.  Its new state is that of having been repainted.  The house became repainted.  In English we use the verb 'became' and the past participle 'repainted'.  We might say having been repainted funtions like an adjective and say for emphasis, "The house became having been repainted."  In Esperanto '-iĝi' is not only a suffix but an self-standing verb whose meaning is 'to become', and we could say "La domo iĝis refarbita.", using the past passive participle 'refarbita' as a predicate adjective (like having been repainted in the English sentence).  Ordinarily instead of "La domo iĝis refarbita." we say  "La domo refarbiĝis."  The suffix '-iĝi' transforms the transitive verb 'refarbi' into an instranstive verb 'refarbiĝi' which indicates that the direct object 'domo' of the transitive verb has entered a new state, specifically the state of having been repainted.

"The house was repainted by my father last month." is the sentence in passive voice which corresponds to the previous sentence in active voice.  In Esperanto we could say "La domo estis refarbita de mia patro lastan monaton.", using a compound verb form.  However, there is very little difference between "The house was repainted." and "The house became repainted."   Instead of using a compound verb form to express the idea of passive voice, it is much more common in Esperanto to use a verb form ending in '-iĝi'.  We don't use the term 'passive voice' to refer to verbs ending in -iĝi, but these verbs do effectively express the concept of passive voice, which is that the grammatical subject experiences the result of an action perpetrated by some agent.

It is important to remember that any combination of transitve verb + '-iĝi' can be replaced the the verb 'iĝi' + a participle ending in either -ita or -ata or by the verb 'esti' and such a participle.  A passive participle is alway understood though not expressed.

   Mi sufokiĝas. = Mi estas sufokata. = I am being suffocated (by something). = I am suffocating.

'suffocate' is both transitive and intransitive, whereas in Esperanto 'sufoki' is transitive only.  The intransitive form does not specify the agent, and in particular does not imply that a criminal act is taking place.

   Mi naskiĝis en 1981. = Mi estis naskita en 1981. = I was born in 1981.

'Naski' is transitive and means to bear (a child), to give birth to.  'Born' is the past participle of  'bear'.

   Usono fondiĝis en 1787. = Usono estis fondita en 1787. = Usono iĝis fondita en 1787. = The US was founded in 1787.
   Ŝtelitaj varoj vendiĝas ĉi-tie. = Ŝtelitaj varoj estas vendataj ĉi-tie. = Stolen good are being sold here.
   Tri aŭtoj ŝteliĝis dum la nokto. = Tri aŭtoj estis ŝtelitaj dum la nokto. = Three cars were stolen during the night.

The addition of '-iĝi' to transitive verbs is very common, and it is important to understand and be able to use this constuction.  The addition of '-igi' to transitive verbs is less important but interesting.