Flatland
Note: You need all four pegs and a gyro for this stuff.
Endo - An endo in commonly known as a donkey kick. Basically, your back tire goes in the air. To do an endo, you roll forward slowly, lean really far forward, push forward and down on the bars, and kind of hop off your pedals. The back end of the bike will come with you. You can also do this while tapping the front brakes. This will get you more height, and take less energy to do.
Bunnyhop - A bunnyhop is where both tires leave the ground. To do one, you just pull up on the front end (preferrably high), push forward and up on the bars, and hop off the pedals a little bit. Your back tire will even out with your front tire in the air. The higher you get your front tire in the beginning, the higher you bunnyhop. Try hopping over all sorts of things. That's how you get better. See how high you can hop.
Rocket Barspin Seatgrab or Tobogen - A tobogen is just where your feet are on the back pegs your right hand is holding onto the seat and you spin the handlebars around 360 degrees. To do one, you just put both feet on the back pegs, slow down until you are at a walking pace, take your right hand off the bars and hold onto the nose of the seat with it, you pull up slowly on the seat and the bars at the same time. Let go of the bars and move your left hand out of the way of the spinning bars. Note: when you pull up, the bars spin on their own. This one takes a lot of practice to land. Just take your left hand and grab the grip when it comes around, take your right hand and grab the other grip (your front tire is still in the air), and land with your feet still on the back pegs. Pedal as normal. If you spin the bars twice it's a Rocket Double Barspin Seatgrab or Double Tobogen, etc.
X-Up - Place one foot on the back peg (right foot, right peg; left foot left peg). Pull up pretty high on the front end, so that the front tire is about a foot to 2 and a half feet high off the ground. Twist the bars half way around (in whichever direction is comfortable for you, it doesn't matter). Twist the back to normal and land. Pedal out.
Frontyard - While rolling forward at a slow/average speed, put one of your feet over the bars (don't put it on a peg or anything, that would just make the next part harder to do). When you feel balanced enough, jump slightly with your other foot, off the pedal and onto the peg. Roll forward like this for a little while (be sure to keep your balance nice and steady). Put the foot in front of the handlebars on the tire and push forward pretty hard. Your back tire should pop up a little. Do this as long as you want to hold it. With the foot on the peg, jump off and back onto the pedal. Pull the other foot back over the handlebars and onto the pedal. Pedal out.
Front Scuffs - While rolling forward at an average speed, put one of your feet over the bars and onto the front tire. Push hard forward with your foot. Continue fir as long as you want. Pull your foot back over the bars and pedal out.
Street
Note: You need a gyro and preferably all four pegs for this crap.
Note: Before doing most of this, you'll want to be able to the first four tricks of flatland. The first 2 are neccesary to do this stuff. And the other 2 just make things more impressive looking when you do them off stuff. It gives people something to look at when they watch you.
Curb Endo - Ride up slowly to a curb. Just as you hit it with your front tire, hit the front brakes and endo. When you get so high you feel like your going to fall frontwards, lean really far back and let go of the front brakes. You'll start to roll backwards. Hit the back brakes and pedal out. If you want to get fancy, you can lean back as you hit the back brakes and spin around 180 degress and then pedal out. Way cool.
Bunnyhop Off Ledges - Exactly what it says. Just ride up to a ledge or curb or something (when your on top of it) and bunnyhop off. You can combine this with things like the Tobogen or X-up to add a lot of style to this simple trick.
Bunnyhop On Ledges - Exactly what it says again. Just bunnyhop onto ledges or curbs or something. If you are really good, you can do some tricks while in the air. Just don't do anything you're not ready for. But it sure does add style to this thing if you do a trick in the air.
Feeble Grind - This is the easiest grind to do. Ride up to a ledge or rail (alongside it) about 6 inches up from the bottom of your pegs. Only try a rail if you're not affraid to fall a lot. Bunnhop and land with your front tire on top of the ledge or rail (only try a rail if you are super good at these) and your back peg on the ledge. Control the bike with the handbars. Ride it until the end of the ledge or rail. And pull up on the front tire. Land with both tires at the same time.
50 50 Grind - Ride up to a ledge or rail (alongside it) about 6 inches up from the bottom of your pegs. Bunnyhop and land with both pegs on one side on the ledge grind along until the end of the ledge or rail. Pull up on the front end and land with both tires at the same time.
Dirt Jumping
If you are going to get even remotely serious about dirt jumping, you need to take off you pegs and front brake first thing. Your pegs don't help you at all when you dirt jump. All they do is weigh you down. And that is not a good thing. You want to be really light in the air. But most importantly, you want some nice burly parts. You don't want to run that light but weak as you know what bull crap they make for racers. You want your frame to be made out of 100% 4130 CrMo (cromoly). Anything less is crap for dirt jumping. Second, you'll want to get hooked up with a set of burly CrMo 3 piece cranks (I would recommend Profile or Poverty). You'll want some 2 piece CrMo jumping bars (if you are running a set of freestyle 4 piecers, that's alright, but I would strongly recommend some 2 piecers. A lot stronger.). They can take a lot of abuse. Most importantly, make sure you have some rims that can handle some hard landings. 36 spoke rims are okay, but if you plan on thrashing your bike day in and day out, 48s are way better (I would recommend Heffer 3's). Be sure your fork is CrMo too. You can get away with an aluminum stem or headset, but it's best to run the strongest equipment you can find when you're jumping. Infact, if you can find it, run some carbon fiber forks. I know Answer makes some. So does BombShell. They are really expensive though. But they're lighter than aluminum and stronger than steel. A carbon fiber fork will run you about $250. Now that we have the gear covered, we can get to the how to part.
X-Up - To do an x-up, level out your feet on the pedals. lean your legs as far toward the back of the bike as you can (so the bars can clear them as you turn your bars). Twist your handlebars 90 to 180 degrees. Bring the bars back to normal position, bring your legs back too. And land. Ride out as normal.