Bevor ich den Kuchen backe, hole ich die Kuchenform aus dem Schrank.

Because bevor is a subordinating conjunction meaning before. In German, a subordinate clause usually sends the conjugated verb to the end.

So:

• Bevor ich den Kuchen backe = Before I bake the cake
• not Bevor ich backe den Kuchen

This is one of the most important German word order patterns to learn.

In a normal main clause, German usually puts the conjugated verb in second position.

Here, the sentence begins with the subordinate clause:

• Bevor ich den Kuchen backe, ...

That whole clause counts as position 1, so the verb in the main clause must come next:

• ..., hole ich die Kuchenform aus dem Schrank.

So the structure is:

• [subordinate clause], [verb] [subject] ...

If you started with the main clause instead, you would say:

• Ich hole die Kuchenform aus dem Schrank, bevor ich den Kuchen backe.

In German, a subordinate clause is normally separated from the main clause by a comma.

So:

• Bevor ich den Kuchen backe, hole ich die Kuchenform aus dem Schrank.

This comma is required in standard German.

Kuchen is a masculine noun: der Kuchen.

In this sentence, it is the direct object of backe (to bake), so it takes the accusative case:

• nominative: der Kuchen
• accusative: den Kuchen

That is why you see den Kuchen.

Kuchenform is a feminine noun: die Kuchenform.

It is the direct object of hole here, and for feminine nouns, the article does not change between nominative and accusative:

• nominative: die Kuchenform
• accusative: die Kuchenform

So even though it is an object, it still stays die.

The preposition aus always takes the dative case.

Schrank is masculine:

• nominative: der Schrank
• dative: dem Schrank

So:

• aus dem Schrank = out of the cupboard / from the cupboard

You use den with some masculine nouns in the accusative, but aus does not use the accusative.

Holen often means to get, to fetch, or to go and get.

In this sentence:

• hole ich die Kuchenform aus dem Schrank

it means something like:

• I get / fetch the cake tin from the cupboard

It is a very common everyday verb in German.

Yes. German often uses the present tense to talk about future actions when the meaning is clear from context.

So:

• Bevor ich den Kuchen backe, hole ich die Kuchenform aus dem Schrank.

can naturally mean:

• Before I bake the cake, I’ll get the cake tin out of the cupboard.

German does not always need a separate future form like English will.

Yes. German very often builds compound nouns by joining words together.

• Kuchen = cake
• Form = mold / tin / pan

So Kuchenform means cake tin, cake pan, or cake mold, depending on context.

Writing it as one word is normal in German.

Yes. German allows both orders:

• Bevor ich den Kuchen backe, hole ich die Kuchenform aus dem Schrank.
• Ich hole die Kuchenform aus dem Schrank, bevor ich den Kuchen backe.

Both are correct. The meaning stays basically the same, but the emphasis changes slightly depending on which part you put first.

Because German often expresses that idea with the preposition aus.

• aus dem Schrank = out of the cupboard / from the cupboard

So German does not need a separate word matching English out here. The idea is already included in aus.

Because each clause has its own subject.

• Bevor ich den Kuchen backe → subject = ich
• hole ich die Kuchenform aus dem Schrank → subject = ich

Even though it is the same person doing both actions, German still normally states the subject in each clause.