Why does my 2000 alero stop running after I start it?

Could be several reasons. Start with checking the basics like fuel and spark. If you're losing spark it could be a bum ignition module or a bad crank sensor. If you're not losing spark, check fuel related issues like a plugged/dirty fuel filter then if the fuel filter checks ok have a fuel pressure test done. Even a bad MAF (Mass Air Flow) sensor could do that. Also, have the ECM checked for codes.