There's a facebook group called "New UW Madison Sublet and Roommate Board". A lot of undergraduates and grads post there to find roommates and sublet. If not, a lot of people also post on Craigslist. The main property management companies are Madison Property Management, Steve Brown Apartments, Keller, Greenbush, JSM, etc.
Generally rents at newer, downtown-located apartments like The Hub, Domain, Grand Central, Lucky Apartments, etc. are pretty expensive and can get up to 1500/month for a studio or 1 bedroom. But if you look for 3+ rooms, they can get pretty reasonable ~500. Also, parking downtown is really annoying and parking spots are highly sought after at about 80-100+/month. I honestly don't think a car is necessary because the bus system is pretty good (you get free bus pass if you're a student) and biking around downtown is also a good option.