There are many ways for your basement to get wet, including busted water pipes, floods and ground water coming in. The important thing to remember when water does come in is that you get it out as quickly as possible. Not only will a wet basement cause damage to your home, such as mold and mildew and wood rot, but it can also cause serious health problems because of the mold. The most dangerous of the molds is a black mold with a scientific name of Stachybotrys chartarum.
Move everything out of the basement in the area where it is wet. Set everything that you can outside in the sunlight to help it dry. If there is carpeting on the floor, it has to come out. Open all windows, if any.
Vacuum up large amounts of water using a wet/dry vacuum. For large floods, consider renting a pump at a tool rental shop. Clean up remaining water using a mop and bucket to get up as much as you can. If the flooding brought mud and dirt in from the outside, you will have to clean up the water, hose everything down and clean it again.
Set up a large fan and direct it toward the wet area. This helps the area to dry more quickly through evaporation. If your walls are paneling or other types of wood, you need to dry those out as well. Set up a dehumidifier to help remove the moisture from the air in the basement, since it will ultimately help in drying the basement out.
Determine the cause of the flooding. Make repairs as necessary to prevent it from happening again. If there are cracks in the walls, waterproof them with masonry caulk. If the problem occurs on a regular basis and comes from the outside, you need to consider having a professional to install drains around the perimeter of the basement and a sump pump.