All good PhDs are funded (if it isn't categorically don't go). Typically this is through advisor's grants, which are usually from the NSF. I'm an international student (originally from India) and I'm funded through my advisor's NSF grant (I think. I'm not 100% sure since I don't know the exact details and he also has some additional funding from other sources like DARPA that he could be using). You should take the fact that I don't really know where my funding comes from as a good sign that PhD funding is very stable.