<p>cookiemom,</p>
<p>There are a lot of reasons why applicants don’t visit in advance, before acceptance/invitation. One is cost. Another is that grad school has nothing in common with undergrad (OK, full disclosure: they both take place on college campuses, although even that is questionable in some disciplines like anthro. 
) so environment, culture and such are approached differently (note choice of words). In fact, kids that are serious about research careers look first and foremost at highly regarded programs and star faculty under which they might work. These kids learn about various programs from undergrad mentors and sometimes can meet prospective grad advisors at regional and national meetings or when these folks give seminars on their undergrad campus. </p>
<p>Further, as juillet suggested, a lot can be learned by email, contacting prospective advisors to find out more about willingness to take on a new grad student. </p>
<p>To put it another way, one either narrows the list in advance through advice from advisors, emails and meetings, or one just applies to a broad list and then evaluates the responses. Most often, applicants do a combination of both, unless they’ve received strong hints that a top choice is pretty likely. (yes, this happens frequently!). </p>
<p>Although much of the grad student support comes from NSF grants, there can still be local differences, often having to do with TAships, promises of research opportunities and such. The details vary widely by field and institution, so it is hard to generalize.</p>
<p>Since shore asked, the better grad programs will pay your tuition and fees, health insurance and provide you with a living stipend of $20,000 - $30,000 per year. Maybe others can correct/update/refine these figures. Many grad students apply for and win portable fellowships in addition to or instead of institutional support. Internationals have a few more hoops to go through and less opportunity on the funding side since some fund sources are restricted to US citizens. So an international student is more likely to be dependent on home country support and outside fellowships.</p>
<p>The key though is that students with star potential will be competed for. More mediocre students may find an acceptance at a second tier school with no support at all. So you get an idea where you stand by what kind of admissions offers you get. That’s one reason why so many grad students delay starting grad school - to upgrade their credentials.</p>