An informal guide to the graduate application process for international students by a former Caltech student, Natalia Lukina, can be found here.
A guide prepared by Prof. Gayle Slaughter (BCM) can be found here.
Additional opportunities for potential/current graduate students:
Lewis-Burke Catalog of Federal Programs that Support Graduate Students
NSF Graduate Research Fellowship Program, deadline: November (US citizenship is required)
NSF Fellowships for Transformative Computational Science using Cyber Infrastructures, deadline: January (US citizenship or GC is required)
Graduate STEM Research Fellowship ($5,000 supplemental support), deadline: February (US citizenship is required)
VEF Fellowship Program, deadline: April (Vietnamese citizenship is required)
Bolashak Presidential Fellows Program (Kazakhstan citizenship is required)
Opportunities for undergraduate students:
RISE Program - summer internship in Germany, deadline: January, no citizenship requirements.
Undergraduate STEM Research Scholarship (up to $8,500), deadline: February (US citizenship is required)
Opportunities for recent graduates (with M.S. and Ph.D. degrees):
Postdoctoral and post-Masterís research associates program at Oak Ridge National Laboratory (most of the positions are open to non-US Citizens).
Useful information for new graduate students (housing, health insurance, life in Charlottesville, etc.) can be found here.