Buy an engine and tear it apart. Nothing will teach you how an engine works faster than disassembling one to see how it works. The engine needn't be a running example, so keep an eye out for broken lawnmowers, weed eaters and other gardening equipment. You'll probably find a few for free if you're willing to ask around.
Research do-it-yourself small engine repair websites, nitro radio controlled car/airplane sites and online tutorials on repairing and rebuilding a specific type of engine. The references listed in this article should get you started. Engine manufacturer websites often contain a wealth of basic information, and online encyclopedias and Internet forums can be equally informative.
Buy a book on basic small engine repair and maintenance. If you have access to a print resource already, focus on learning the basics of four-stroke engines before you get into two-strokes. Four-stroke engines are more complex but require a less in-depth understanding of engine dynamics to understand. Check the resources section of this article for some suggested reading.
Attend a small engine repair course at your local community college or vocational school. This step probably isn't necessary if you're only learning to build and repair engines for your personal use, but it may be a prerequisite if you want to get paid for doing it.