Turn off the power to your basement and wait until the water around your house has receded. Use external pumps to remove about a third of the water every day until the water is low enough for your sump pump to handle it. Removing more than a third of the water per day may weaken and crack the house's foundation and cause your basement to reflood.
Turn the basement power back on and run your sump pump if you have one. Put on your gloves, goggles and respirator. Use a shop broom or floor squeegee to push large water puddles towards the sump-pump hole. Open the basement's doors and windows if you have them.
Run the wet/dry vacuum over the basement floor to take care of smaller puddles. Put down disinfectant on the floor to help kill bacteria and get rid of any odors from the flood water. Empty the wet/dry vacuum as soon as you are done to prevent bacteria and odor problems in your vacuum.
Place as many fans as you can in the basement and turn them on. Do not turn on the central air or heating, as this can dry out and further damage the building materials.
Use a dehumidifier and run it 24/7. Turn off the dehumidifier when the catch bucket is full and empty the catch bucket. Replace the bucket and turn on the dehumidifier again. Attach a hose to the dehumidifier if possible to run it continuously without having to repeatedly empty the catch bucket.