Hola Sue

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.

Saludos

Inma

Hola John

There are certain verbs that undergo vowel changes when they are conjugated in the present. These verbs aren't grouped depending on how they are written. It is random verbs. So these two verbs "poner" and "poder" both have stem-changes but different ones:

Poner (to put)

Yo pongo

Poder (to be able to)

Yo puedo

I hope this helped.

Inma