i mean, you could remove the seat cover and foam to let them air dry, but that might be a bit much for a DIYer. most seats use hog rings to hold the cover in place, and they can be a bit difficult to reinstall (plus you need specialty pliers). also, there are often rods in the foam that they clip around, which can be easy to rip out accidentally.
best solution is probably a strong shop vac and then drying in open air. may help to pull the seat out of the car and put it somewhere warm and dry, if it's really soaked.
edit- if this is a newer car and you do take the seat out, remember not to turn the key on while the wiring is disconnected from the seat, or you'll set an air bag light.