You need to pass TOEFL (English) test in your country and a proof that you (or your parents) have about $10K for you to start studying (some colleges require less, some more). Then INS gives you student visa and usually you can easily find job on-campus for $7-8 per hour (cafeteria, gardening, cleaning, etc.) for not more than 20 hours/week, which will help you to pay for education.
Some colleges may ask you to pass SAT or ACT with some minimum score, some their own (lower-lever) test to let you in.
Because main problem with a foreign student is a language, first and most important is to pass TOEFL in you own country. Different colleges may require different TOEFL score.
Details are usually on the web page of each university, in the "foreign students information" or something like that section . So, just type "usa colleges" - there are enormous amount of them -like 10^3 around USA (among which there are 10-20 good universities, 100-150 so-so and tons of community colleges which usually are less than so-so, BUT community colleges can be an easy trampoline for a new foreigner to jump to higher University in a year or two, after he learnes more English and will not be destructed by hard homeworks - and they all offer TRANSFERABLE basic courses in math, physics, chemistry, biology, astronomy, genetics, English, etc.).
If you want to be cosmologist/ astrophysicist/ astronomer, then you HAVE to take college algebra, calculus, trigonometry, differential equations, physics, chemistry, computer modelling, basic astronomy, quantum mechanics, special and general relativity BEFORE you will start specialized study in astrophysics, and that study usually comes in graduate school (AFTER you get your 128-credit-hour bacalaure degree in physics, which usually takes 3-4 years). Most colleges offer all those basic courses, so you may graduate practically any of them with physics degree and then go to good university which has strong astrophysics program. Courses there will include vector calculus, tensor analysis, calculus of variations, PDA (partial differential equations), special and general relativity in depth, quantum electrodynamics, quantum chromodynamics, particle physics, plasma physics, lasers (quantum electronics), cosmogeometry (multidimensional geometry) and a few specific subjects of local astrophysicists who teach in that particular school (it can be black hole theory, galaxies formation, universe dynamics, etc..,). Also, in graduate school, especially on PhD level you HAVE to do research under some professor who is doing specific cosmological or astronomy problem - and this is usually computer modelling (of regular and neutron stars, supernovae, galaxies collision/dynamics, or it can quantum gravitation models, multiverses, etc) or observational astronomy - to travel from time to time to scopes of various size mostly across USA, sometimes to really big ones in Hawaii or Chili, and in rush taking data (in a few short nights which were given to you after a year wait). And then back to you home lab where you spend tons of time processing your images or spectra on a computer (and discovering a lot of things which went wrong during shooting) and in preparation for next shots a few months away.
It is wery exiting career, but if you want to succeed in it, it requires to learn a LOT of math and to have a strong character (will) to do plenty of homeworks. And the earlier you start doing some research (some colleges have some kind of student research programs even on bacalaur level), the easier will be for you to get into graduate school, because professors in graduate schools just love to have recommendations which mention research interests and espesially research results of future graduate student.