First, some definitions:

A flooding basement is when there is standing water in the basement to a level of 6" or more.  Basement flooding usually occurs when there is general flooding, like when a nearby river overflows its banks and there is standing water on the ground outside the house.  The only way to avoid flooding is to raise the entire grade level of the house, which is not usually possible.  If you live in a flood plain, it is highly recommended that you get a house on higher ground.  There is no real solution to flooding.  The house was simply built in a place where it should not have been.

Most times, basements do not flood, but have seepage.  Seepage is when your basement floor gets wet, when the carpet in the finished portion of a basement gets all wet or when floor drains or basement sink drains back flow because of the large amount of water in the storm sewers.  Basement seepage is easily avoidable, and easily cleaned up when it does happen.

Make sure that your roof's downspouts are in good condition and that the drain at least 6' away from the house (12' is better) and that they drain down slope from the house.  The grade around your house should, ideally, slope away from the house at a rate of 1" down for each 12" away.  This is a quick, easy and inexpensive solution.  If rain water is drained away from the house, it will not come back into the basement.  Very simple, but the most overlooked solution, in my experience.

Make sure that you have a good quality de-humidifier in your basement (65 pints per day capacity, or better) and run it 24/7 all summer.  Buy a model that has an optional drain hose option.  This will allow the water to drain directly into a floor drain and save you the grief of having to empty the de-humidifier when it gets full.  Even if you don't have seepage problems, you can still have high moisture levels in your basement (finished or not).  Your house's foundation and basement slab are cooler than the rest of the house.  They are underground and the ground is cooler.  During the summer, when there are high humidity levels, this humidity will condense on the foundation walls and slab and produce moisture.  Use of a dehumidifier will also keep down your air conditioning bill.  Dryer air feels cooler than humid air.

If you have a full pr partially finished basement with carpet on the floor, make sure that you have a 6 mil plastic vapor barrier between the carpet pad and the slab floor.  When you think about it, a carpet pad is just a big sponge.  This sponge will soak up any condensing (or seeping) water and wick the moisture right up to your carpet.  Eventually, mold will form and you will have to replace the carpets.  Install the plastic directly on the concrete slab floor.  Overlap the seams or the plastic sheeting at least 6" and tape them.  Bring the edges up the walls, at least 2", and install the baseboard over the plastic.  Also, make sure that basement carpets are made of synthetic materials, like polypropylene.  These materials are much less prone to mold and, if quickly dried (within a couple of days) can be re-installed.  There are even some newer products that allow a small air space between the slab and the floor, which will still keep the carpet dry but will also allow for ant condensation to be air dried  (See here: www.dricore.com ).

Make sure that any drywall walls in your basement are properly installed.  The bottom of the drywall should be installed at least a 1"" space above the concrete floor.  This gap will keep water from wicking up the drywall and will help to keep it dry.  If your drywall was not installed correctly, it is usually easy to just cut out 1' at the bottom.

Make sure that your sump pump, if you have one, is equipped with a battery backup power supply.  Many of our past clients have ignored the recommendation to install a battery backup.  Their basements got wet.  Power failures usually occur along with rain storms and the time you most need your sump pump is when it is raining.  In addition, there are special back-up pumps that can be installed beside the regular pump.  These back-up pumps will provide extra drainage flow if there is a large amount of water draining into the sump or in the case of your main sump pump failing.

Before you finish your basement, make sure that all of the small, vertical cracks in the foundation wall have been properly sealed.  It is not a good idea to purchase a new house with the basement already finished.  As new houses settle, they will develop a few small cracks in the concrete foundation.  This is normal and to be expected.  These cracks are best fixed by a professional foundation crack contractor and using high pressure polyurethane foam injection.  I have never seen such a repair fail and most contractors give 50 year warranties.  Once these cracks are sealed, the basement can be finished.  Just make sure that the contractor who finishes the basement properly insulates the walls and installs the required fire stops.  Remember, cheap contractors do cheap work, which is very much more expensive, in the long run.

ASAP, make sure that there are no electric wires that are under the water level.  Also, make sure that you are extra careful with electric devices in wet basements.  If you have standing water (flooding) in your basement, disconnect the main electrical switch or call your local fire department to do it for you!  Only use double insulated and grounded vacuums and dehumidifiers.  If you are in doubt about the electrical safety of your basement, stay out of it!  You can live through the water damage but not through being electrocuted.

As soon as possible, suck up the water with a Shop-Vac and get some extra de-humidifiers running.  Your air conditioner should also be running (it also de-humidifies).  Keep the windows closed.  The idea is to get the air in the house, and especially in the basement, as desert dry as possible as quickly as possible.  This dry air will draw moisture out of the walls, carpet and other areas.

Take off the basement wall baseboards and drill 1" holes halfway between the wall studs at the base of the walls, about 2" off the floor.  When you re-install the baseboards, they will cover these holes.   The holes will allow moist air from behind the drywall or paneling to be dried as the de-humidifiers suck out the humidity.

If you do get mold growth, do not use bleach to clean or kill it.  The EPA has determined that bleach is not an effective fungicide and bleach puts out harmful fumes when used in large quantities.  There are much more effective (and less harmful to humans and pets!) fungicides available at the major home stores.  Spray them directly on the affected areas and let them kill the mold.  These products will soak into the wood and drywall get to the roots of the mold, killing it completely.

When all is dry (keep the basement windows closed and run the de-humidifiers, usually, for about a week or two to ensure complete dryness), it helps for your to call a licensed and certified home inspector who is also specially certified perorm do mold testing.  If you can hire an inspector who is also specially trained in thermal imaging, that will help to verify that the basement is fully dry.  Ask the inspector for a mold clearance test, which ensures that mold spores are not present.  Make sure that the inspector does not do mold remediation.  This could lead to a conflict of interest.  If there are mold spores present, call a professional, licensed and certified mold remediation company.  When they are done, have the area re-tested by an independent inspector.