I'm just repairing them for the fun and education of it Im 15 so I don't know a whole lot but I want to learn about them.
Micah, the best way to learn about small engine repair is to just find old engines and take them apart and put them back together and figure what makes them tick. Work on how they come apart and go back together. You will figure out the diagnostics about what is wrong in the process. From there you start thinking what could be wrong when an engine won't start or what cause an engine to run poorly. Or if you have an engine with a broken rod, figure out what caused the rod to break. Did it break because the engine didn't have oil, or maybe dirt wore out the rings, and caused oil consumption leading to low oil failure, or maybe the governor has failed causing the rod to break due to overspeed. The pro technicians, like Rivets says, use the manuals in sections as more of a reference than how to work on something. Most of the service manuals are written for the basic tech that has some formal training, so they will not tell you have to remove a part or reinstall a part.
A little background about myself. My parents would go around the old junk yard, and bring the lawnmowers home for me to take apart when I was 3. I didn't ask for toys for christmas, I wanted tools. Started reassembling engines when I was 4, did my first overhaul on my parents 5 hp briggs tiller engine when I was 5. Was working on larger engines by 10, and was doing all the mower repairs for my family by that age. As I got older just kept at it to get to where I am now. One of only two briggs MST's in IL to have past the old 4.5 hour paper test on my first attempt without attending the Briggs factory school first. Keep in mind that this test had a first time failure rate of 80%. some techs in the business that had worked on engines for 40 years couldn't pass the test in 5 attempts.
To get good you have to remember what you have learned, and keep track of the odd failures, because they may come in handy in the future. Even failures on automobiles can be relevant in some cases, especially when it comes to EFI on lawnmowers. Just finding mechanical knowledge no matter what the source can be handy sometimes. Be it cars, tractors, ATV's, boat motors, can all be applied to small engine repair.