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I agree that the best way to learn is through some hands-on practice: whether it be a lawnmower, dirtbike, etc. The key is to have something already complete and running. Also, try finding a manual for the equipment you're working on. The Honda and Suzuki manuals I have are really good as a reference. I find myself reading them just for fun sometimes. You'll soon learn that working on many machines are very similar, but there are certain specific tools/procedures for some jobs.
I also agree with what was said above about dealing with bolts. This is something that comes with experience. My general method is to use a torque wrench when the bolt is large (chassis bolts like axles, shocks, etc.), "critical" for function (head bolts, fork pinch bolts, etc.), but tend to use my instinct and feel for other bolts especially smaller ones (anything with plastic threads, ornamental pieces like bodywork). For ratchet/sockets: try to use the size appropriate for the bolt size. For example: for smaller bolts use a 1/4" drive ratchet and hold your hand over the "head" of the ratchet kind of choking up on it to avoid overtightening. For medium size bolts use a 3/8" drive, and larger bolts use a 1/2" drive. Shouldn't need anything bigger than 1/2" unless you're working on heavy duty machinery. Get a breaker bar for bolt removal too, which will help prevent busted knuckles, as long as you have room to swing it. Be aware of materials/designs of the bolts/threads. Softer metals will strip easier, less threads will strip easier, phillips head screws will strip easier than Allen heads, etc.
As suggested above, start with the maintenance stuff first then move onto more complex jobs as you gain experience and confidence. Read how-to's, watch videos, and just ask questions on forums before perfoming anything you're unsure of. It can save a lot of trouble. Be patient and take a break if you get stuck on something. If not, you'll spend more time fixing a mistake than you would have if you just waited for some advice or to get the proper tool for the job. Use PB Blaster or similar on stuck/corroded bolts in advance of trying to remove them. A little heat from a propane torch can go a long way in helping free stuff up, but be careful around aluminum and plastic (to not distort or change their mechanical properties) and fuel sources, of course. Vise grips are good to have around, but only use them when you don't have the correct wrench/socket and you'll be able to replace the nut/bolt with a new one.
Over time you'll learn more about the finer details about machinery. Things like which sealers to use (don't use regular old RTV sealer for stuff in contact with fuel or high temp stuff like exhausts), when to use Loctite and which strength (use Blue, temporary variety for fasteners that will see a lot of vibration or are saftey related and that you'll be removing at some point), cotter pins, what parts to grease or use assembly lube on.
In addition to putting bolts back where they came from as you disassemble and laying out the parts in order, use zip lock bags and label them. I like to keep subassemblies separate. You always think that you'll remember the parts and where they go, but projects get put on hold and you'll forget. So take pictures and stay organized. Good luck!