There are a several different ways of doing this, and how you do it will depend in part upon the rules or guidelines of your tradition. If you're a solitary, or your tradition is eclectic, then you may choose the method that works best for you.
Typically, when an area is ritually purified, it is done in a clockwise, or deosil, direction, but this may vary from one tradition to the next.
Smudging
With smudging, you can use sage, sweetgrass, or other herbs. You can also use incense, if you like. The purpose of smudging is to use smoke to carry negative energy out of the area. When you light sage or sweetgrass, allow it to flame for a moment and then blow out the flame. This will leave you with a burning herb bundle, which will create smoke.
Asperging
In some cases, you may wish to use asperging as a method of cleaning a space. Asperging means using liquid -- the power of water -- to purify the area. Although this is typically done by sprinkling consecrated water around the perimeter of the space, you can also asperge with milk, wine, or either of these blended with honey.
Sweeping
Typically, the broom is associated with cleaning and purification. You can use a broom or besom to go around the edges of the space, sweeping negativity away as you go. It's a good idea to start and finish near a door, so that negative energy can literally be swept outside.
Salt
Salt has been used for purification for thousands of years. Use a bowl of sea salt, sprinkled around the area, to cleanse the space and make it sacred.
Fire
In many cultures, fire is used to ritually purify and cleanse a space. You can do this by lighting a candle and walking the area, or sprinkling cooled ashes around the perimeter