You can start by vacuuming the upholstery but if there are any stains it will be hard to remove them without at least a damp cloth. You could try sprinkling on baking soda, letting it sit to give it time to work, then vacuuming the residue. You could also get a spray upholstery cleaner from an auto department or store. Those are designed to work then be vacuumed off, but they do go on wet so they will need drying time. Check the label to see how long that will take. You could also try just a damp cloth to see if that's enough to pick up any spots. That would dry quickly. Wishing you the best with your cleaning.
if the seats are leather, buy either leather cleaning wipes or ones used for leather seats - you can find them in walmart and grocery stores ~ if they are fabric they also have cleaners for fabric seats in the automotive dept of walmart that works really well for carpet and upholstered seats
Blue Magic and Blue Coral are stain lifters made specifically for car upholstery. Blue Magic is made by the Chemical Guys, I personally love their products. Both are available at auto supply stores.
If you have access to a wet/dry shop vac, after vacuuming it with a soft bristle brush,
then I would have a friend run the shop vac in wet mode, after I sprayed a cleaning solution on it.
The cleaning solution I would start with is five drops of Woolite in a quart of warm water. Use the (cleaned) soft bristle brush on it and vac out the water & residue.
When clean, spray with warm water only, for a rinse cycle.