Don't be anxious! Madrid is a big and cosmopolitan city where is very easy to fit in.
Ciudad Universitaria is a district where most colleges are placed. It's to the northwest of Madrid, and 15 minutes away from the town center by subway.
You know enough spanish to deal with most situations. Besides, spaniards are very tolerant with language problems (we are very used to tourists, and appreciate any effort made to speak spanish).
where to do laundry: there are plenty of laundries along the city. I'm sure you won't have any problem to find one. Ask your neighbours where to find one! They are called "lavanderías" or "tintorerías".
what to do during the day: visit museums, monuments, walk through the city, try some restaurants, go to the theatre, to the cinema, have a swim bath in a local swimming-pool, look around the shops, go to a bowling, to discos or pubs,...
how best to practice my language skills: speaking with anyone you have the chance to!
how to meet people: that's tricky, depends completely on your social skills. Start with your neighbours and your class mates
I'm sure you'll have a great time here! Enjoy!
Fernando