1. Start with a list
Colleges put out a list of what to bring, and what NOT to bring to the dorms. Don't waste your money buying anything on the "What NOT to bring" list, as it will likely be confiscated.
2. Coordinate purchases with your roommate
Check with your roommate, prior to move-in, to see what they already have that you can share. Split up any remaining items that need to be purchased. For example, one roommate buys an ironing board, while the other brings an iron. One roommate brings a power strip, and the other brings a hair dryer. You're not going to have room for two of everything.
3. Use what you have
Check your home for things you already own that are on the list. Last year's backpack may hold usable school supplies, and the garage or attic is a great place to find forgotten home goods. You may find that you have some or most of what you need. Keep an open mind, and don't be afraid to repurpose old items. Flat sheets make great curtains, milk crates make excellent storage cubes, suitcases can make great underbed storage, etc......
4. Hit up friends/family
Put the word out that you need to furnish your first place, and that you're open to hand-me-downs. You never know who has an extra bookshelf/microwave/desk, etc...collecting dust in the garage that they no longer want.
5. Turn trash into treasure
Cruise by dumpster in apartment buildings around the first of the month. Apartments have a high turnover rate, so someone is always moving out. Some good stuff is usually left near the dumpsters by residents who just didn't feel like moving it. If you think dumpster diving is demeaning, just think about how much beer you can buy with the money you'll save!
6. Shop thrift stores, craigslist, and garage sales
You'd be surprised at how many new or almost new home items you can find in a thrift store for a fraction of the price. Cheap furniture can regularly be found on craigslist or at garage sales. Don't forget to negotiate!
7. Shop sales, and use coupons!
If you've exhausted all your other options, and still have things that need to be purchased, don't forget to shop sales and use coupons!