Picture that you are standing inside a compass with your skis pointing north. Let's assume you only spin left in the following examples:
Cork: you lean southwest or west and spin. You aren't supposed to go fully inverted. If you do, it's called a D-spin
Rodeo: you lean east/southeast and do an off-axis backflip with spin
Flatspin: similar to a rodeo, but instead of going completely inverted, you strive towards doing a horizontal flip. Picture that you jump on to a table and start spinning around on it.
Bio: you lean northeast. Don't go fully inverted, or it will become a misty.
It's often hard to tell the difference between rodeos and flatspins, and flatspins and bios. Many an angry verbal battle has been fought in the threads of newschoolers trying to riddle out the correct name of a trick. Use this as a guide and you'll be fine.
Bonus:
Underflip: flip south and spin left. Usually a 540, or a 900 in the double flipping version. This is a trick that will get you laid if executed well.
