Fuel, Spark and Air. You need those three.
Checking for spark is easy, unplug the spark plug, unscrew it, connect it to the cable again now its out, touch the end to the frame. Now crank the starter. If it does anything other than spark across the base of the electrode to the arm, get a new one. (Try not to zap yourself, its not pleasant)
Fuel (with a carb) is usually a case of undoing the float bowl release and seeing what comes out, if anything. You may have a clogged pre-filter or inline filter. You could remove these (temporarily), or use an easy-start type aerosol starting fluid to get it going as a test.
If its fuel injected, you should be able to hear the fuel pump click/prime when you first turn it on. Listen for a whirring. If nothing, could be a fuse for the pump, or a dead/clogged pump. If it does not stop whirring/clicking, its likely not getting enough/any fuel, so check the fuel tank pre-filter, or inline fuel filter (same process as mentioned above)
Air, check the airfilter does not have a rats nest in it, or is full of dust. You could remove it if you are not sure, as a temporary measure.
If you have all these things working fully, a full charge from the battery, and it still refuses to start, then you have a bigger problem (worn rings, bad timing, dropped/worn out/bent valves, or a badly blown out gasket)
This is over simplified, and there are other things it could be, but assuming it was running when it went away, it should get you some of the way, if not all the way to getting it started following the above.
Apologies if I miss anything stupid, I have been up way too many hours to have written this out any better
Edit, or just bring it to me, and I will figure it out for you....
