There are internships available in the major offices (well, DC and Chicago anyway). I don't know the specifics of how to apply, though. It likely depends on the specific area of interest you have (internships are generally related to your field of study or career goals, not just a part-time summer job). I don't know what colleges would use an internship as a criterion of whether or not to accept you, as generally, you get into college first, then get an internship.
Ironically, when I do a google search for "Amtrak Internship" the first three results are threads on this forum.
Also, as a word of advice to you and anyone else who is hoping to get a job with a particular company (whether it be Amtrak, a transit agency, or anyone else out there), do be careful in what jobs you apply for (that is, only apply for postings that you actually want and actually think you might be qualified for). In a former job, I had to go through applications that people submitted to work in my department (not Amtrak), and for some reason the application packet included a listing of every job that individual had *ever* applied for at the company.
There were some people who had literally applied for every job listed on the website, from janitor all the way up to some VP positions. We actually used that to filter applicants out, as it was obvious that they weren't really going for the job we were hiring, they were just desperate to get a job.
I'll echo what others have said in that you aren't going to get a position in maintenance or operations just as a kid out of high school looking for a summer job. If Amtrak is a company you want to work for longer term, find an area that really interests you (it doesn't hurt to study something of a related field when you go to college), then try and get the name of a manager that works in that department and ask him/her about the possibility of an internship.