You will be prompted to start the MotoSkills the very first time you play the game. If you declined the prompt the first time, then all you have to do is press Y at the menu screen.
MotoSkill 4: Take-offs and Landings - "Use Rider Reflex to achieve massive air and critical landings."
Just hold down the gas and back on the right thumb-stick, and jump the double in front of you twice.
MotoSkill 5: Wreck Avoidance - "Learn how to stay in the race while avoiding painful wrecks."
All you have to do is attempt to jump the double. You will always fail to clear it, and immediately a greenish arrow will pop up on one of the four sides. You will have roughly two seconds to move the right thumb-stick in the direction indicated.
MotoSkill 6: Freestyle Tricks - "Learn how to pull off insane tricks."
To do tricks, hold the left bumper and move the right thumb-stick in three directions while in the air. However, to complete this MotoSkill, you have to do three specified tricks. The first jump you will have to move the right stick up, down, then up (a Shaolin). The second jump you will do down, left, then up (a Supercan). The third and final you will do left, down, then up (a Deadbody).