I have rubber floormats and hate it when it rains because the floor always gets wet. I get leaks from my cowel vent, dashboard, doors, windshield, etc. Most of it has been replaced with new rubber but it'll still prone to have some leaks.
Run a water hose over your vehicle beforehand and find where any of the trouble areas are when it comes to water getting inside. I guess you can use caulking water sealant on some areas to make sure it's waterproof.
Other than that, depending on how much water got it, leaving a kick vent open during the day might be enough to air out the rig. On really rainy days I'll take out the floor mats to dry out completely as I also have the sound deadening mat, which holds in a lot of moisture.