Sudden appearances of water on your basement floor could mean literally anything. Without a clear-cut idea of where it is coming from, how do you know which type of repair you need or which type of contractor? With something that baffling, you have to start with what you know; contractors that frequently handle watery things.
Usually, leaks and puddles of water in your basement mean that your water heater, pipes, or boiler (if applicable) are responsible. You could call a plumber first to see if the plumber can find the source of the problem. If it is plumbing-related, great. The plumber can fix it. If it is not plumbing-related, the plumber can tell you who else might be able to help.
Air conditioners frequently use evaporators to turn liquid into a gas, and condensers to condense the amount of gas and liquid before turning on the refrigeration component to cool it all. If a hose from your air conditioner is leaking, that liquid is not getting to the evaporator but is instead pooling on the basement floor. If your air conditioning does not seem as cool and refreshing as it should, that would make perfect sense. After the leaks in your air conditioner components are found and repaired, the water issue should go away and your air conditioning should be quite comfy again.
Water Well Drillers
Certainly, you do not need a well in your basement. However, if you have cracks in your basement's floor, or you have a really old dirt (i.e., soil) floor instead of concrete (and some homes still do!), the water may be coming up from a natural well below your house. The water well driller can take a peek by doing an exploratory small bore drilling. If he/she finds that there is an aquifer under your house, that may explain why you have so much water pooling on the surface of the floor. Of course, you should only resort to asking this type of contractor if both the plumber and the HVAC technician cannot find the source of the water or the water returns after the plumber and the HVAC technician have already completed their repairs.
Foundations are funny things. You may not notice or see any cracks anywhere, but the water keeps pouring in and collecting in your basement. A concrete contractor knows what to look for if the problem is with your foundation. Then the concrete contractor can contribute his/her field of expertise to find the cracks and fill them.
Contact a local air conditioning repair service for more information and assistance.