Americano - This is Espresso and hot water.
Cafe au lait - 1/2 coffee, 1/2 milk.
Cafe breve - 1/2 coffee, 1/2 1/2 and 1/2 (confused? Same as cafe au lait but with half-and-half instead of milk.)
(Caffe/Cafè) Latte - These are both two syllable words, and it basically refers to espresso with a lot of milk.
Cafe latte macchiato - Hot milk with a teaspoon of espresso.
(Caffe) Mocha - This is espresso with a hit of (usually dark) chocolate. This can be very bitter but have a deep flavor.
Cappucino - 1/3 Espresso, 1/3 Milk, 1/3 Frothed Milk (bubbles!)
Espresso - Coffee + extreme heat + a lot of pressure = CAFFIENE!!!
Another thing to consider is the type of roast, if this is an option. In order from sweeter to more bitter there are: Cinnamon, American, French, Spanish, Italian. Of course there are many others, but these are enough to remember. (If you leave out "Spanish", maybe C.A.F.I. is an easy acronym to remember.)
That should be enough, but feel free to post some extras in the comments, and I might add a few.