Here are good techniques to dodge red and green turtle shells while racing.

To dodge red shells, put a banana behind you, by either dropping it there or holding it there. When the red shell collides with the banana, its effects will be nullified, allowing you to proceed with the race unhindered.

To dodge green shells, use the same technique as listed for the red shell above if the shell is coming straight at you or is bounced off a wall. In other situations, use the three-shell weapon. Red or blue shells will protect you from the green shells in these situations.