Medium-density fiberboard, or MDF, is a wood product manufactured by breaking down scraps of soft or hardwood, mixing them with wax or resin, and baking and pressing them into a dry, boardlike shape. MDF is much cheaper than natural wood products, but is heavier, not as strong in most cases, and highly susceptible to water damage. MDF can only be dried out if it is not exposed to water for a very long time, and in most cases it will be warped by even short exposures.
Use a dry mop and absorbent pieces of cloth or even paper towels to get the water out of the particle board as quickly as possible. The longer the water sits in the board, the greater the damage will be, and in some cases the board may start to break down if it soaks too long. Also, keep in mind that a thoroughly soaked board will be warped, even when completely dry again.
Set up fans all around the area to move as much air as possible over the boards, which will help pick the moisture out of them.
Use a heat gun (or hairdryer if you don't have a heat gun) to dry out the boards even faster by slowly and evenly passing it back and forth over the wet boards. Make a pattern like you're mowing a lawn, back and forth in alternating directions as you move along, and when you've gone over all the areas start again from the beginning. You want to dry the boards quickly but evenly so as not to warp them even more than they will be already.
A better, though more expensive option than the above would be to rent a heat-drying system, which will be able to pump a lot more hot air for a longer amount of time than a heat gun combined with fans. The basic principles are the same though: Warm the air so it can pick up more moisture, and keep it moving over the wet floor.