In this sentence: "¿Me pone un café, por favor?, you need to conjugate it in the 3rd person singular (usted). "Me pone..." is an idiom used when you order something in a bar. It would be the equivalent to "May I have...?" or "I'd like..."
When we use this structure, you must think of the literal translation in Spanish which is:
Do you put me a coffe, please?
I know it sounds really weird but this is one way to order something in a bar in Spain.
So, "pone" is poner conjugated in the 3rd person singular formal for usted, "do you put...?
I hope this clarified it.