How do 'rejections' typically happen?
phone? e-mail? letter? both?
Unfortunately, it depends on the school. I have received personal emails from SC heads, Emails from admin assistants with form letter pdfs attached, formal letters through the post, and sometimes nothing at all.
Agree with the above, it varies a ton. Plus even if they sent a rejection, you would not be notified for quite some time. They will only send out official rejections after a candidate has signed an offer — not when the offer is made. So, it could be a while before you even hear anything.
With that being said, if you know when the last candidate visited and you haven't been notified of anything within a week or two after that, then in all likelihood you were not the SC's top choice.
I usually receive a form letter by e-mail or by postal mail. In rare cases, the SC chair will include a personal note. Sometimes the letter comes very late, long after I've given up on the search (e.g., letters received in June for jobs to which I applied in the previous October). Other times I never get a letter at all.
Edit: I should clarify that this is for applications in general. After a campus interview, my experience has involved receiving a personalized e-mail.
If you've gone on a campus interview and haven't heard for a few weeks after their last interview, I think it's acceptable to contact the SC chair and ask them for an update. (If you have another offer, you obviously have a good excuse to ask. This happened to me last year. I told them I had an offer elsewhere and asked for an update, and they told me their first choice had verbally accepted their offer.) Other than speaking with them personally to find out (always initiated by me), I've never received anything more than a form letter later. (Which I consider pretty rude, given that you spent at least a day getting to know them personally.)