Vor dem Auftritt lerne ich den Dialog auswendig.

German often puts a time expression first for emphasis or flow. When that happens, the conjugated verb still has to stay in second position.

So:

• Vor dem Auftritt = first element
• lerne = second element
• ich = comes after the verb

That is why you get:

• Vor dem Auftritt lerne ich den Dialog auswendig.

You could also say:

• Ich lerne den Dialog vor dem Auftritt auswendig.

Both are correct. The first version emphasizes before the performance a bit more.

Because the preposition vor takes the dative case here when it means before in a time sense.

• der Auftritt = nominative
• dem Auftritt = dative

So:

• vor dem Auftritt = before the performance/appearance

This is a very common pattern in German:

• vor dem Essen = before the meal
• vor der Prüfung = before the exam
• vor dem Konzert = before the concert

Auftritt can mean a performance, appearance, or stage appearance, depending on context.

In this sentence, it most naturally means something like:

• performance
• appearance on stage

So Vor dem Auftritt suggests a situation like an actor, student, or performer preparing before going on stage.

Den Dialog is the direct object of the verb phrase auswendig lernen.

The noun Dialog is masculine:

• der Dialog = nominative
• den Dialog = accusative

Since the person is learning the dialogue by heart, Dialog is the thing being acted on, so it takes the accusative case.

Auswendig means by heart or from memory.

So etwas auswendig lernen means:

• to memorize something
• to learn something by heart

Examples:

• ein Gedicht auswendig lernen = to memorize a poem
• Vokabeln auswendig lernen = to memorize vocabulary

A useful contrast:

• lernen = to learn / study
• auswendig lernen = to memorize

It behaves like a verb phrase with a separable element in normal sentence use.

That is why in the sentence you see:

• lerne ... auswendig

The two parts split in a main clause:

• Ich lerne den Dialog auswendig.

In an infinitive form, they stay together:

• Ich will den Dialog auswendig lernen.

You may also see auswendiglernen written as one word, especially in dictionaries or infinitive form, but in everyday sentence structure the split form is very important to recognize.

Because in a main clause, the conjugated verb goes in second position, and the separable part goes to the end.

So the structure is:

• Vor dem Auftritt = first element
• lerne = conjugated verb
• ich = subject
• den Dialog = object
• auswendig = separable part at the end

This is a very common German pattern:

• Ich stehe früh auf.
• Sie kauft im Supermarkt ein.
• Wir rufen dich später an.

Yes, it is in the present tense:

• ich lerne

But in German, the present tense is often used for:

• habits
• general facts
• scheduled future actions
• near-future situations

So this sentence could mean:

• Before the performance, I am memorizing the dialogue.
• Before the performance, I memorize the dialogue.
• Before the performance, I will memorize the dialogue.

The exact interpretation depends on context.

Yes, if you mean a dialogue rather than the dialogue.

Compare:

• Ich lerne den Dialog auswendig. = I am memorizing the dialogue.
• Ich lerne einen Dialog auswendig. = I am memorizing a dialogue.

Using den suggests that the listener already knows which dialogue is being talked about.

Yes, Dialog is a normal and common German word.

It is usually pronounced approximately like:

• dee-a-LOG

with the stress on the last syllable.

English speakers sometimes expect something closer to dialogue, but German Dialog is shorter in form and does not end with -ue.

Not really. The word auswendig makes the meaning specifically about memorizing or learning by heart.

Without auswendig, the sentence would be more general:

• Ich lerne den Dialog.
  This could mean I am learning/studying/practicing the dialogue.

With auswendig, it becomes much more specific:

• Ich lerne den Dialog auswendig.
  = I am memorizing the dialogue.

Yes. Vor is a two-way preposition, which means it can take either dative or accusative, depending on meaning.

• Dative: location or time

  • vor dem Haus = in front of the house
  • vor dem Auftritt = before the performance

• Accusative: movement toward a position

  • Ich stelle mich vor das Haus. = I move to a position in front of the house.

In your sentence, vor expresses time, so it takes the dative: vor dem Auftritt.