First, check compression. It doesn't tell you everything about a motor's condition but it's a good indicator that a motor is worth fixing or not. Best case: I would be pleased if all cylinders are within 10 psi of each other and compression 120psi or better. I could live with at least 100psi compression and all cylinders within15%. Below this, I'll tinker with it but I don't expect much.
Second, verify spark. Spark testers can be had for under $15 at your local auto parts store. If no spark, you have to work your way through the electrical system. There are lots of kinds of ignition systems - you'll need to find the instructions for troubleshooting the one specific to your engine.
Third, verify that you have fuel in the carburetor's fuel bowl. There is probably a screw you can remove on the side of the bowl and you should see fuel pour out. Or, remove the bowl and see if it has fuel in it. This proves that you have fuel at least to the carb, even if it isn't getting through the carb to the engine.
If you have good compression, good spark, and fuel to the carburetors, my next guess is dirty, plugged, or varnished (from evaporated fuel) carbs. I would remove them, disassemble them, clean them, and replace any jets, floats, float needle, seals, or other parts that seem questionable. After rebuilding, find instructions on adjusting the air idle screw on your carb. Usually, you turn it in to gently seat (valve now closed) and turn it out 2 full turns. Hopefully, the engine runs and you turn it in or out until you hit the sweet spot where it sounds the best at idle.
If you can feel air blowing OUT of the carbs in puffs when the motor is turning over - suspect damaged or bent reed valves - this is unusual but it happens.
Lots of other things can go bad but I think this covers the most common issues.