Things that really wear out tires:
Burnouts- Take your time to make sure you don't burn out your wheels at the start of a race or after a really sharp turn
Taking turns too fast- Just look at them when you're on a really sharp turn and you go too fast. They will quickly turn from blue, to green, to orange, and then red if you do too many of those.
Braking really hard- Just like turning too hard and burning out, you go too fast! Try to slow down a little bit before you floor the brakes.
Unbalanced tires- No, you can't really balance them as you would in real life, but find out by the power and the drivetran which tires burn up first(if any), and then get some more slick(hard) tires on them. Then if you get the right balance, they should stay the same throughout the whole race.