A wet crawl space can use vents or install a sump pump. Your first step is to prevent water from accumulating in a damp crawl space. Find any source of rainwater, either from gutters or low ground around the building and raise the grade so water drains away. If you do not get rid of the surface water, you will never dry up the crawl space.
Once the surface water is controlled, the crawl space will start to dry up. Then you can mix a little bleach and water, one part bleach to four parts water, and spray in the area to kill off any mold or mildew. Do not put yourself in harms way and get trapped in the crawl while spraying the bleach.
My next plan is to dry and warm the crawl space area. Eliminating surface water will dry up the crawl, adding some heat, and keeping it, will make the room above warmer and easier to heat.
When the bleach has dissipated insulate the perimeter of the crawl space. Use a nonflammable foam-board (at least one inch thick) against the block walls inside the crawl. Do not insulate the wall adjacent to the basement.
To do this, excavate a few inches of dirt from the perimeter of the inside of the crawl. Use a garden hoe or short army shovel to make a shallow trench at the base of the foundation. Then cut the foam so it fits from the dirt trench to the bottom of the floor joists. Tack a few nails into the bottom of the joists to hold the foam at the top. Then push the dirt to refill the trench and hold the foam at the base.
Then stuff the floor joists with fiberglass insulation around the perimeter of the room. Cut pieces of six-inch fiberglass into twelve-inch lengths and stuff them on top of the foundation wall between the joists. Two pieces per joist space is even better.
Next, vent the crawlspace into the basement. This will allow cold air to pour out, while warm lighter air replaces it. This requires creating an opening or two between the crawl and the basement. Sometimes an old window provides one of the openings. When possible keep the holes as large and as far apart as possible. The exact limits of these two openings will require some professional guidance so you do not compromise the integrity of the building. A quick meeting with a licensed builder will also prevent you from breaking local building codes.
Opening the crawl space to the basement will allow several things to happen. One, the moisture from the crawl will combine with the basement air and in time the crawl will dry up. Two, the room above the crawl will be easier to heat once the crawl space air warms to the basement temperature.