Dopo aver finito il compito, mi preparo per uscire.

Because Italian uses the past infinitive here: dopo + aver + past participle.

• aver finito = having finished
• So dopo aver finito il compito means after having finished the homework/task

This structure is very common when the subject of both actions is the same:

• Dopo aver mangiato, esco. = After eating / After I’ve eaten, I go out.
• Dopo aver studiato, mi riposo. = After studying / After I’ve studied, I rest.

Using dopo finire would not be correct in standard Italian for this meaning.

Yes, but the meaning shifts a little depending on the tense.

• Dopo che ho finito il compito, mi preparo per uscire.
  = After I have finished the homework, I get ready to go out.
  This is very close in meaning to Dopo aver finito il compito...

• Dopo che finisco il compito, mi preparo per uscire.
  = After I finish the homework, I get ready to go out.
  This can sound more like a habitual or future-related statement, depending on context.

The original sentence with dopo aver finito is compact and natural when the same person does both actions.

Aver is just a shortened form of avere.

• avere = to have
• aver finito = to have finished

Italian often drops the final -e of infinitives in certain structures:

• dover fare
• poter andare
• saper parlare
• aver finito
• esser partito

So dopo aver finito is completely normal and standard.

Finito is the past participle of finire.

The structure is:

• avere
  • past participle
• aver finito = to have finished / having finished

This is the same basic idea as other forms:

• ho finito = I finished / I have finished
• dopo aver finito = after finishing / after having finished

So finito is there because the sentence refers to an action completed before the next one.

Because with avere, the past participle usually does not agree with the direct object when the object comes after it.

Here:

• aver finito il compito

The object il compito comes after finito, so finito stays in its default masculine singular form.

A learner usually only needs to remember that in normal modern Italian, with avere, agreement is often not shown unless there is a preceding direct object pronoun, and even then it is more of an advanced point.

So in this sentence, finito is exactly what you expect.

Because prepararsi means to get ready, while preparare usually means to prepare something.

Compare:

• Preparo la cena. = I prepare dinner.
• Mi preparo. = I get ready.

So:

• mi = myself
• mi preparo = I prepare myself / I get ready

In this sentence, the person is getting ready to go out, so the reflexive form is the natural one.

In Italian, reflexive pronouns usually come before a conjugated verb.

So you get:

• mi preparo
• ti prepari
• si prepara
• ci prepariamo

This is normal word order in Italian.

But with an infinitive, the pronoun can attach to the end:

• prepararmi = to get myself ready
• voglio prepararmi = I want to get ready

So in your sentence, since preparo is conjugated, mi goes before it: mi preparo.

Per + infinitive often expresses purpose in Italian.

So:

• mi preparo per uscire = I get ready in order to go out / to go out

Other examples:

• Studio per imparare. = I study to learn.
• Vado al supermercato per comprare il pane. = I go to the supermarket to buy bread.

Here, per uscire explains the purpose of getting ready.

Sometimes learners wonder about this because English often uses to.

In this sentence, per uscire is the most straightforward choice for expressing purpose: getting ready in order to go out.

Prepararsi a + infinitive can also exist, but it often gives a slightly different feeling, more like getting ready to do something imminently or preparing oneself to do something.

So:

• mi preparo per uscire = I get ready for the purpose of going out
• mi preparo a uscire = can be possible in some contexts, but is less neutral here

For a learner, prepararsi per + infinitive is a safe and natural pattern in this kind of sentence.

Because Italian usually drops subject pronouns when they are clear from the verb ending.

• mi preparo already tells you the subject is I
• The -o ending signals first person singular

So (io) mi preparo is possible, but io is usually unnecessary unless you want emphasis or contrast.

For example:

• Io mi preparo, tu resti qui. = I get ready, you stay here.

In your sentence, no emphasis is needed, so leaving out io is natural.

Compito usually means homework, assignment, or task, depending on context.

So:

• in a school context, il compito often means homework or assignment
• in a more general context, it can mean task or duty

That’s why the sentence could be understood as:

• After finishing my homework, I get ready to go out or
• After finishing the task, I get ready to go out

The exact translation depends on the situation.

The comma is natural and helpful because the sentence begins with an introductory clause:

• Dopo aver finito il compito, mi preparo per uscire.

It separates the after... part from the main action.

In informal writing, some people might leave it out, but using the comma is a good habit here because it makes the sentence clearer and easier to read.

Yes. The sentence clearly shows that one action happens before the other:

1. finire il compito = finish the homework/task
2. prepararsi per uscire = get ready to go out

That sequence is expressed by dopo aver finito = after having finished.

So the person does not get ready first; they finish the task first, and only then get ready to go out.