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If you are asking this question, my feelings are that you may not be very good mechanically, because a lawn mower engine is about as basic as they get. My suggestion to you is to take it to a lawn mower repair shop and have them go through it. The jets in the carb are probably varnished up from gas evaporating while stored. It will need soaked and cleaned out.
The fact it ran when you introduced some fuel into the combustion chamber tells me that you have spark but fuel is not getting through the carburetor. Very common problem on stored small engines.
It shouldn't cost a fortune and if you use an ethanol treating stabilizer (Stabil, or Startron, for example) you shouldn't have this problem next season.