There are many different methods, as you've said, for propagating... much depends on the plant that you are trying to propagate, some are ridiculously easy, like the basil that I stuck in a glass of water on the kitchen counter to keep fresh and now has roots. Or the red-twig dogwood that a friend cut some branches off to make a little border fence for her flower garden, and it all ended up growing into new bushes... Others need much more pampering! I don't personally have a lot of experience with starting the more difficult plants, but would like to "branch out," so to speak -- did you have any particular species in mind?
This is such a broad topic that I think we may need a whole forum for "plant propagation."