College towns have predictable patterns when it comes to housing. Things get very competitive at the start of a new term, such as in September or January. Time your apartment search towards the end of terms. May and June are your best bet.
Be prepared for rental applications that ask some in depth financial questions. You will also be expected to verify this in many cases. This means that just saying that you have a job won't be enough. You may be asked to provide a letter from your employer or you school explaining your financial situation.
Busses and bicycles are both your friend while in Burlington. The Chittenden County Transportation Authority operates busses in Burlington and the surrounding cities. They provide an affordable way to get quickly around town. Bike lanes and slow moving traffic makes a bicycle a safe and quick way to get around the town. There are a handful of shops that rent bikes if you want to try before you buy.
Downtown Burlington is worth visiting even if you're just passing through. There is a beautiful walking market and stores and restaurants in many historically preserved buildings. Lake Champlain provides a scenic waterfront and the perfect place to enjoy water-based activities. Magic Hat Brewing Company is a sure-fire bet fore beer lovers. Finally, Burlington likes to throw parties all year long, including the Winter Carnival, a Jazz Festival in June, and a Brewers Festival in July.