Make sure you have good basement drainage, as it is essential to your having a dry basement. There are four ways that moisture can enter and collect in basements and sometimes two or more are happening at the same time. If your home was built on a high groundwater table and steps were not taken to move the water away, water can wick up through the concrete floor and walls. Rainwater or melting snow can leak in through flaws or openings in the basement walls. A poorly ventilated basement may have condensation causing the moisture. Leaky supply lines or drainpipes are always a possibility. Find the source of the moisture and if you cannot, hire an expert in basement construction.
Check your basement floor drain to ensure that any water can flow away from your home. If your house was built on a high groundwater table, you will most likely require a basement sump pump to raise the water to a level that can drain away. Efficiently removing any water is the absolute first step in creating a dry basement. Now if leaky pipes are the source of the moisture, it is relatively easy to have repaired. Call a plumber. Rainwater or melting snow needs to be directed away from the walls of the basement. This may be only adding some pipe to your down spouts. If this does not solve the problem, you will need to check the perimeter basement drainage to see that it is able to function as it was designed to. In a high groundwater zone another sump pump may be require here. If condensation is the culprit, you will need to address the proper ventilation of your basement.
A dry basement is your goal if you wish to have a healthy home. This may require sealing the concrete to stop seepage in from the surrounding soil. It may require adding a basement sump pump to your basement drain so as to remove any water that makes it into the basement. You may need to dig the soil away from the outside of the basement walls and fixing the peripheral drains and adding to the down spouts. Or it may just require fixing a leaky pipe. Whatever it requires, this is what you will want to do for the health of your house and that of your family.