How do I properly prep and cook chicken thighs?

(If a moderator gets a chance to delete the other version of this, I wasn't expecting "Enter" to submit...)
I'm just flummoxed by how my favorite General Tso's chicken (or a number of other restaurant items) have chicken thighs so that they're delightful all the way through. I find when I try to prep them, it's all but impossible to remove all the bits that look suspect to me (membranes, etc) without reducing it to a few strands of meat, and if I'm not thorough enough, it's all goingy bits and unpleasant textures.
I'm missing something; I tend to avoid it by substituting boneless, skinless breast meat for almost everything, but that's not the ideal solution.
I know there's more than one way to cook them, so I guess while examples would be good, a more general understanding of what they require would be even better.