Thanks, everyone, for the good advice. When I first started, I did copy from others' trees, but at this point I have gone through the process of getting support for pretty much everything. I've used what I see in others' trees to see if they can point me in a direction.
I've felt extremely puzzled when looking at some people's trees -- there's stuff in there that isn't logical or that just cannot be true. I think they're just blindly copying other people's stuff, which I sure haven't been doing, and then you see the same mistake perpetuated over and over.
My biggest headache right now are two of my great-grandfathers, both German immigrants -- I can find them in censuses and city directories and such, and I have the naturalization certificate of one grandfather, but I cannot find them in any of the passenger lists, and in the one case, I have not a clue of what his city of origin in Germany is, so I'm completely stuck there. But I will keep plugging along with it, because I'm hooked, and find the whole thing fascinating and very satisfying.