Anytime you go on the edge of a slope, press R or Zr as soon as you go off the edge to get a speed boost. You can also achieve this by shaking the controller.

When you get a throwable item like the green shell, pressing L or Zl and moving the camera where you want to aim, you can snipe them!

When youre in first and you have a super horn or mushroom, save these items as you can dodge the blue shell with them. For the super horn, when the blue shell comes around you, press the item button (L or Zl) to dodge, and with a mushroom, you use it when the blue shell stops above you.

When on a rail, press R or Zr when you see blue sparks coming from your wheels. If you trick into a pole or tree, it does a trick for you and you get extra distance and hight.