Assess the extent of the water in the basement. If your basement has tiny puddles of water, use a dry towel or a mop over them and drain excess water into a bucket. Keep doing this until all the water is soaked away and collected in the bucket. Open windows to allow fresh air to come inside, and turn the electricity back on so you can run a fan to dry up the floor.
Rent a sump pump if you do not own one for a major flooding with several feet of water in the basement, draining out 2 feet of water every 24 hours. Pumping more aggressively could weaken the outside soil, causing the basement to cave in. An alternative to a sump pump is to use two or more portable small pumps, but make sure you connect these to a large diameter drain hose or garden hose. Also remove the water as far away from your house as you can to prevent it from reentering the basement. Begin pumping either from the section of the basement that will sustain the most damage due to floodwater or from the highest point where the accumulated water is at the lowest level.
The amount of days it will take to remove all the floodwater from the basement will depend on its size and the amount of accumulated water. It could take anywhere from one day to several days since you will not be draining out more than 2 feet every 24 hours. Once all the water is removed, turn on the fans and open all the windows to dry out your basement. Prevent opening windows if it is raining outdoors, and work with fans only. You can also use a dehumidifier to dry the basement, but make sure all the doors and windows are shut before you turn it on.