Put a throw rug on the floor if the room isn't carpeted. Carpets absorb sound and so help reduce incoming noise as well as sound you make that might disturb your neighbors.
Hang curtains. Windows allow a lot of noise from the outside to come into your room, and heavy curtains block such sounds. This also allows you to personalize your room a bit. If the rules allow, hang drapes or attach heavy fabric to the walls and even the ceiling of your room to absorb noises from other students. Check the dorm regulations about attaching products to existing structures; be sure you don't cause damage when you hang objects on the walls.
Place furniture such as dressers and bookshelves against shared walls to muffle sounds, if you are lucky enough to have a dorm room large enough for furniture.
Purchase a white noise machine or noise-canceling headphones to block out noise you can't stop with other methods.
Talk to your resident assistant, resident hall director or housing director if noise levels continue to be too high.