My ATV isn't starting - what is it?
 

So last time I tried to start my ATV (prob like 3-4 months ago) it was turning over and firing but wouldn't start, as the reduction gear was missing a few teeth, enough that the starter would slip and it wasn't turning the engine over fast enough.

Anyways fast forward to know, I replaced the reduction gear - but it is just turning over and not starting. I don't think it is a spark plug because I have no idea how to fix a spark plug, and also, there is no reason it would have stopped working (it just sat, nothing happened to it). The gas I put in may not be as high octane as the one I used to have in it, but I don't think that would cause it to not run. And I know the carb is working, because the air it pumps out of the exhaust smells like gas, and if I put my hand in front of it for a while my hand smells, too. What can it be?

If you have fuel you need to check for spark or just take out the plug and put a new one in. Valves might also need adjustment. There are good videos on YouTube.

Could it be it needs a carb clean?

That is possible. You said there was fuel coming out the exhaust. Might be the float sticking on. Check spark and also spray fuel in the carb to see if it will try to fire. Look at the plug and see also if it's wet with fuel. Order a plug and a spark checker and a valve adjustment tool.. You need a few basic cheap tools.

You definitely have to check for spark. If it's cranking over and you smell gas but it's not firing it's likely a spark issue (or compression). That being said, it's almost impossible to diagnose issues over the internet, youtube is a very valuable resource and you will be able to get a better idea of what to look for when you are troubleshooting.