What actions can I take to reduce moisture on basement floor?
Multi-part answer here:


It could be the water table, in which case, there's not a lot you can do.  If it's the water table, then you'll have water seeping up through the floor. BUT consider that when they built the house, they dug a bowl in the ground, and then backfilled with loose soil, rocks and whatever other garbage they had lying around.  You could have a permeable (gravel and sand) fill inside a relatively impermeable bowl (clay).  In this case, sloping the ground away can help.  It will at least get rid of standing water up against the foundation and help mitigate anything flowing through the walls.
The major worry is mold.  Make sure the area is clean, so that there's nothing for mold to feed on.  You can spray with a biocide if you see any growing, and certainly don't enclose it by adding drywall over the area.
If you have rising damp, then an internal sealant won't do anything.  the hydrostatic pressure will force water through.  A dehumidifier will remove the symptoms.