Mazda MX5 - 03 1.8 Drying out a wet car - Bromptonaut
As others suggest, absorb as much as possible using old towels, newspaper etc.
If you can lift carpets and get newspaper underneath that will help too. If areas of carpet can be removed bring them inside to dry - did this with our Xantia's boot carpet after it started to ship through a join in the plastic tailgate.