Soundproofing means increasing the materials between you and outside sources of noise. Windows carry sound more easily than walls. Walls deaden sound, but don't cut it completely. Most homeowners don't like to use professional sound-deadening materials because they're unattractive. Common household items can be used to reduce sound. Hanging heavy drapes and installing double-glazed windows reduces sound. Thick carpet on the floor reduce sound. These ideas can also make the room more energy efficient.
If room aesthetics are a secondary concern, using professional sound-deadening materials is a better solution than drapes and carpets. There are many types of studio foam and sound-deadening materials, and they can be purchased online or at music stores like Guitar Center. Basic foam looks somewhat like an egg carton. There are materials that are designed for specific frequencies that can greatly improve the sound in a room. Most of these materials can be purchased by the foot or yard.
The best option for soundproofing is to create a "room-within-a-room." Essentially, you build a secondary wall about a foot out from the original and fill the space with soundproofing foam. You'll also need to build a secondary ceiling and fill the space between it and the original with soundproofing foam. You can either hire someone to do this for you, or, if you have carpentry and framing skills, do it yourself.