Apply for fellowships. NSF, NDSEG, and Hertz are all open to anyone in the sciences, and there are some other fellowships that are more field-specific. In general, you should only really care about the fellowships that provide full tuition (as opposed to the many smaller fellowships that offer ~$5k-$10k per year).

Fellowships usually don't actually help your personal monetary situation that much, but dramatically increase your flexibility to do what you want in grad school.

Background: first year PhD student in machine learning at Stanford.