That is a great learning tool, Brian. You'll learn really quick with it...that you don't like it, that is...
Actually, I've made a couple of "mugs/steins". But this was before my turning days. I made segmented mugs, with long strips of wood with 22 1/2 degree angles on the long sides. Just lay down some masking or painters tape (say, 3 strips). Lay the wood strips with the angles already cut on them across the three strips of tape, making sure they abutt each other nicely. Put glue on each of the angled surfaces. "Roll" them up! The tape acts like your clamp, but also keeps them aligned. Once dry, remove excess glue. True up the bottom and top on a good sander or on a miter saw. Make a bottom that fits the outside shape of the mug. Glue it on!
NOTES: Do all your sanding beforehand. Finishing the strips can be done beforhand as well, but you'll likely have to do a little touch up if nothing else afterwards anyway. (I did all my finishing afterwards.) I finished mine with poly. Make sure you give it LOTS of time to dry before using it. You can use contrasting woods to make it look neat. I've walked around with mine at parties and Ren Fests, and the like. Gets lots of compliments. People tend to remember you from year to year by it. Make sure to bring it back the next year, or you'll get a hard time for NOT bringing it...
Whether you do it segmented or turned, enjoy!