If your floor is inside, check your water table. If so, contact a professional to see what can be done to prevent water from seeping in. Exterior concrete surfaces should have a natural runoff slope so that water doesn't collect in one spot. If the surface remains wet all the time, it's not suitable for decoration. Thoroughly clean the concrete.
Grease is the most common barrier to paint.
To remove grease, put down cat litter to absorb the big chunks, then scrub again and again with Goof Off. Then, mix up a bucket of TSP and scrub the floor, rinsing several times, until your mop is clean. Wait three days for the floor to dry. Remove any visible nails. Repair cracks and holes with Cement Fixall.