So I shaved my legs for the first time this morning, or tried to 
Most of it isn't coming off! The hair feels very fine, and I think the razor is just bending it and passing over rather than actually cutting. Has anyone else had this problem? How do you get around it?

Part of my thigh shaved nicely and I feel great! Not being able to do the rest is driving me a little crazy 

get a better razor and also try to shave the same spot multiple times , that should do it.

Sometimes if hair is stubborn at coming up, I will go over the area with the trimmer that is built into my electric razor (Panasonic ES2207, the little pink and white wet/dry shavers for like $30 at Walmart). I go against the grain with the trimmer and the hair it doesn't get will end up sticking up and be much easier to get with a normal razor.