Place a thick throw rug on the floor of the space you want to record in. Even if the area is carpeted, the added material will help absorb even more sound.
Close any doors and windows in the area. Make sure you have the curtains closed to block out as much exterior noise as possible. This will also help to dampen interior sounds.
Cover the walls with blankets from around your home as free soundproofing option. Or purchase soundproofing foam to put on the walls as a relatively inexpensive form of soundproofing. Covering the walls will reduce the vibrations bouncing off of them, cutting excess noise.
Scan the area for any cracks, crevices and unfilled holes in your soundproofing system and fill them with either extra pieces of the soundproofing foam or even towels or washcloths from your house.