Things to try
I've been through this a few times! Here's what I would try in order of easiest to hardest. First check for a spark using a new plug, connected, but grounded outside the engine. If no spark, then it could be the coil, plug cap, hi tension wire, points, condenser, wiring, or stator coil, in other words, a lot of stuff to check. It could be just the timing is WAY off, but ironically, most two strokes will fire or backfire if the electrical system is fair but the timing is way off. You can't inspect the condenser to see if it's OK, and it's not easy to tell if the points are ok by looking. Best to just replace both points and condenser with new parts, then carefully set the timing by the book.
If you've got a nice spark and it's not running, move on to the carb. After kicking it a BUNCH, pull the plug and see if it's wet. It should be wet, and smell like gas. If it's dry, take the carb off and take it all apart carefully. You can do a careful cleaning of all the deposits and the misc jet, but sometimes it's just faster and more sure to buy a rebuild kit for the carb.
Nine times out of ten, it's either the ignition system or the carb. If those check out, things get more complicated...