There's a bunch of videos online with a demo of drinking.
Specifically for coffee you can watch that here:
According to this post, he uses a special cup that has a specific shape and surface tension.
During STS-126 last November, mission specialist Don Pettit devised a
cup that took advantage of its special shape and surface tension such
that it was perfect for use in microgravity.
This special object is actually just a report cover.
As Pettit describes in the video, the plastic for the cup was taken
from the cover of a flight data file, so I stopped by an office supply
store and purchased a report cover. In orbit, Kapton polymide tape was
used to hold the cup together. Despite my best effort, I was unable to
find a local store that stocks Kapton, so another 3M product, Scotch
tape was substituted (if I ever come across a few strips of Kapton, I
will use it to cover the clear tape).
oddly enough there was an article written yesterday (July 15th, 2013) on this exact question, pointing out the same information and same video.