MIT has a special FIRST YEAR MAKER training program, which combines a safety orientation and a short manual or digital fabrication training class. On completion you receive access to the Metropolis and The Deep makerspaces, a cool tool box, a T-shirt, and $50 Makerbucks to spend on materials. Not a First Year? No worries! You have access to the same ORIENTATION, TRAINING, and MAKERSPACES.
MIT has many student-run makerspaces, such as Miters and MakerWorkshop.
Shops like Edgerton and the MAD N52 Shop are open to anyone who wants to join. Explore the shop page to see if it's a good fit for you.
Some makerspaces are associated with a particular Club or Team, and some require a membership like the MIT Hobby Shop, but these may be a great fit for you depending on your interests.