At US universities students can earn money in exchange for assisting with research or teaching. At MIT this means that the professor for whom you are an RA or TA will pay your tuition fees as well as a small stipend. In order to TA a class you will almost certainly need to have taken it the previous year, which pretty much rules being a TA out for 13-month students unless you have hard core experience in that area – but 17 month students should seriously consider this as some of the more common Spring classes are also taught in the Fall, e.g. to Sloan.
The sort of 'research' conducted by an RA may be as straightforward as preparing lecture notes, doing literature searches, or drafting teaching cases so don’t be put off by the grand title. Oddly enough being a TA is slightly better paid than being an RA, and also is thought to be an easier workload by most people. In order to get a TA or RA you need to get in touch with the professors yourselves. This is a very daunting process if you have yet to even reach MIT, especially if you are new to the US university system. Ask the SDM office for assistance in placing you and be flexible.
Since you are usually on campus (not many professors are prepared to give a TA/RA to a distance person), you have access to take extra classes and go to seminars. A TA/RA is only supposed to take two classes a semester and so extra classes must be negotiated with your RA/TA professor, but usually have not been a problem. You can always audit rather than taking them for credit. Research sometimes requires you to travel, which then means finding video conference facilities or watching classes via videotape. Videotape, for most classes, is not a great option; for others it is fine, you have to talk to earlier year's students to find out which are which. In 2001 traveling researchers sometimes dialed in by telephone only – it can work provided it is not the norm, and is certainly cheaper.
If you are thinking of paying your way through SDM with TA/RA posts then be aware that most professors are not used to paying for a TA/RA in the Summer. Also make it clear to your professor that there is an extra tuition fee for SDM in the first 13 months (it covers the January program costs, the business trips, etc.) so that they are not taken by surprise by the slightly higher than normal tuition bill.
Discuss with your professor where you will work. One of the advantages of being on-campus is that you can help build the SDM community, but if your professor wants to lock you up on the far side of campus then, whilst you will still benefit you will not be as able to easily interact with other 13/17-month or visiting students.