Learn Russian: Повтори свой текст, перед тем как выходить на сцену. - Repeat your text before going out on stage.

When the subject of the main clause and the "before" clause is the exact same person (here, the implied "you"), Russian usually follows перед тем как with an infinitive verb rather than a conjugated one.

Is there a difference between using перед тем как and до того как in this sentence?

They are generally interchangeable, but перед тем как often implies that the first action happens immediately before the next one. This makes it perfect here, as you are reviewing your lines right before stepping out onto the stage.

Why does the sentence use свой instead of твой for "your"?

In Russian, whenever the "owner" of the object is also the subject of the sentence (in this case, the implied "you" of the command повтори), you must use the reflexive possessive pronoun свой rather than твой.

Could I use the perfective verb выйти here instead of the imperfective выходить?

Yes, both are grammatically correct here. Using the imperfective выходить treats "going on stage" as a general routine or process, which is very natural. Using the perfective выйти would shift the focus slightly to the singular, completed result of stepping out.