For a speed boost as a race starts in venom, flash and phantom (no rapier) DO NOT hold X before the race starts. Instead, click X when it says GO. This will give you a speed boost as if you were on one of those blue arrows. You have to know exactly when to press X so it takes time to get used to it. Make sure you don't crash into the ship in front!
To unlock the Beta League in any Ship Class, beat the Alpha League with 3rd place or higher. When you beat the Beta League, you'll unlock the Ascension League. Beat the Ascension League to unlock the next Ship Class level. This doesn't apply to Vector, however, as you automatically start out with it and Venom, and Venom is already unlocked. You have to do the same thing for each Ship Class to unlock the next, harder Ship Class. Here are the Ship Classes in order:
Vector Venom Flash Rapier Phantom
Each race gets faster and faster. I guess they upgrade your ship's speed thrusters to tune with the race, huh?
When you are rounding a corner at high speed, use your airbrakes to slide more easily around the corner. To use them, hit R to engage the right airbrake, and L to engage the left airbrake, or hit both to slow down evenly. You will lose a little speed by using airbrakes, but usually you will lose more speed by slamming into the wall and taking a good chunk of damage than by using them.
While airborne after flying off a ramp, press Left Right Left in mid-air either on the D-Pad or the Analog Stick to make your ship do a Barrrell Roll that will give it a speed boost when it hit the ground. If you press Left Right Left, your ship will Barrell Roll left; if you press Right Left Right your ship will do a Barrell Roll right. The further you fall through the air after doing a Barrell Roll, the better the speed boost. Oh, and one more thing... Doing this trick requires you to lose a little health.