How can i find out what is wrong with my 1999 chevy tracker 2.0l.,when it runs for a while it wont start untill it cools,and back fires

It's either crankshaft or camshaft sensor. Once it warms up it breaks down and won't start until it cools.

Ignition module or coils may be heat failing.

Go to Autozone or one of them and get the trouble codes read. Probably something there, maybe a crank or cam position sensor code, or also could be something in the ignition system like a bad coil or the ignition control module. The ICM controls the ignition coils' circuit, both of these two items can go bad and then fail when warmed up. Backfiring, shaking, and coughing kinda sounds like a bad crank sensor, but that's just a guess. Check for trouble codes first.