Learn French: Est-ce que tu peux prendre une photo de moi ?

peux is the conjugated form of the verb pouvoir (can / to be able to) that goes with tu (you). Both je (I) and tu (you) use the form peux in the present tense.

Why is prendre (to take) left in its basic, unchanged form?

When you use pouvoir with another verb to say you "can do" something, only the first verb (pouvoir) changes to match the subject. The second verb, which is prendre here, stays in its basic dictionary form (the infinitive).

Why does the sentence start with Est-ce que instead of just asking "Peux-tu" (Can you)?

Placing Est-ce que before a regular statement is the most common way to ask a yes/no question in everyday French. While you can swap the verb and subject to say Peux-tu (Can you), that sounds much more formal.

Why does the sentence end with de moi instead of using the word me?

In French, whenever a pronoun comes immediately after a preposition like de (of/from) or avec (with), you must use a "stressed pronoun". The stressed pronoun for "me" is moi.