"Me pone un café" literally is "(You [formal]) put me a coffee".
Remember that with the formal singular "you" form ("usted") the endings for 3rd person singular are used. So it's like "él ponE" --> "usted ponE".
As for where this sentence is used, it can also be used in other shops--basically in any shop where you would ask the shop assistant (sales clerk) to serve you something.
I hope this helps!
P. S.: I would say people most frequently use this sentence as a question, so "¿Me pone un café?", which sounds more polite.