Dress for the part. This is going to be a messy job, and you will get wet. Don't wear your Sunday best to drain out your crawl space.
Plug in your wet/dry vac and set to work, vacuuming up as much of the water as you can. If you don't have a sump pump in your basement, you can drain the water through your bathtub or, less preferably, your sink. Be careful when draining the water and avoid spilling it on your floor or counter tops as much as possible.
Set up fans and a dehumidifier to help dry the wet spots on the ground when you're finished vacuuming it up. The dehumidifier will suck the moisture out of the air and help prevent mold growth.
Turn up the heat in your home to help dry the air and clear out any remaining moisture.
Use towels to block any leaking points and monitor the area closely until you get the leak repaired.