Check for spark first using the grounded plug method described previously. You should get a nice blue spark. ( make sure the gap is set correctly) If you have spark, move on to fuel. If the spark looks weak ( yellow or hit & miss) check into the points (if it uses them) and condensor.
If you have spark, put the plug (dry - no fuel) back into the cylinder head. With the switch turned off and the choke on, give the thing 5 or 6 good pulls on the cord. Pull the plug again and see if its wet. If it is, sniff it to make sure its gas and not water.
If the plug is still dry, clean the carburator, FUEL LINES, FUEL FILTER, and air filter. If the old gas was left in the carb for the year, your probably going to need to disassemble it and cleat it good, including the float and needle valve orafaces. Re-assenble and try again to see if your getting fuel.
If you have spark and fuel, I would go to timing - but - you say it was running when you put it away last season. So I would next check the valves ( you say it had better compression after you shot some gas in the cylinder ) and make sure one is not stuck (or bent). If the valves are ok and it still feels like no compression you probably have collapsed piston rings which means a teardown.
Best method I've ever found to get um working is to take er to the shop and pay the man. Otherwise, the snow season will be over before you get er started.