Student Exchange Programs

I need some information about international exchange programs. I’ve checked out several sites and looked through the Yahoo answers as well, but I really need some specific details that aren’t readily available.

Are there any programs for American students traveling to other countries that run for three months during the school year? (For instance, January through March.) If yes, are only specific countries and/or organizations involved or are there a lot options?

Also, if the scenario I just described does exist, how far in advance would the student need to apply for the program? When would they find out if they’ve been accepted? Specifically, if they were to leave in January, where in the process would they be the summer before?

Thank you for any insight you can offer!