It depends on two things. First, what city are you going to? For a city with a tighter housing market (e.g. DC from personal experience, and I assume places like SF and NYC) you need a longer lead time, like two months. Second, what sort of housing are you looking for? Usually professionally-run apartment complexes will want a little longer lead time (between 1 and 2 months depending on the market), while small landlords like you'd find on Craigslist often don't list the apartment until it's actually open, so you can go as little as 2 weeks ahead of time - of course, then you run the risk of not finding a place in time.
[For example, in DC - tight market - I always found professional places 2 months ahead of move-in, while renting from an individual would be about 1 month or maybe less. In St. Louis, it looks like the time frames are ~1 month for professional places, 2 weeks for individuals. If you want to grab a place earlier than that, you'll likely need to pay rent for at least some of the time you're asking them to hold it for you.)
Unless you're planning on buying a place, you don't need to start looking until the summer. But if you don't know anything about the housing market where you're going, I'd start looking into it around May or June - see what the prices are, call apartment complexes and see how long of a lead time you should allow, etc. Hopefully your school will provide you with some information too.
