There are many reasons why a basement may be wet. The first order of business is to determine if the water is coming from inside or outside the home. By that I mean that if you have a clothes dryer in the basement that isn't vented outside properly, you have humidity from the appliance causing or adding to the problem.
This is quickly fixed by simply venting the offending clothes dryer outside. There are many ways that this can be accomplished but remember that a dryer vent should be no more than about 25 feet in length total figuring double the length for each bend. So if a 90 degree bend which is somewhere around 12-15 inches in total length is involved, you would count that bend as 24-30 inches of the total 25 feet allowed.
Just as a side note, dryer vents are a leading cause of house fires so be certain to clean it regularly. I do mine twice a year. Once in the spring and another time in autumn when the time changes. This happens also to be the time I change all the batteries in the smoke detectors also.
Here's a good tip: Remember that water seeks the path of lease resistance.
This means that you can't just check the area where you think the water is coming into the basement. The water may be seeping into the ground many feet away then traveling against the outside of the basement wall until it can get inside. Be sure to check all around your home for water seeping suspects!
If the moisture seems to be coming through the concrete side walls, this usually indicates a drainage problem outside. Check all the gutters and downspouts. Check to see if the downspouts are long enough to move the water well away from the foundation of your home. If you find short extensions on the downspouts or possibly just an elbow dropping the water on a concrete pad, it's a good bet at least some of your basement moisture is coming from here. A quick run to the store to pick up 10 foot lengths of landscape piping and this suspect is finished. The pipe is cheap and can effectively move the water well away from your home.
Another place to check is the grade of your property. The grade is the angle of the ground from the point where it touches the house and runs out away from the structure. This should be a minimum of 1/4 inch to the foot though the greater the grade the better water is sheeted away from your home. Be sure to check everywhere around your home including the deck. Many decks even of concrete have settled over the years causing water to actually collect back close to the house.
If after checking the grade around your home and fixing any suspected gutter downspouts you are well on your way to getting a dry basement.
If water seems to be seeping from the floor of your home, this can suggest several problems, all of which probably are best left to professionals. These include special drains and drainage strategies to move water away from your home faster. French drains are a good example of a usually effective water handling strategy.
Finally, there are also some very high quality waterproofing coatings and products on the market. These may be used if the major causes of the water leakage have been found and corrected.