Couple things I do as I have some nice expensive gear.
Dry everything out. If you have time at the camp site great , but if you are backpacking or need to leave camp right away then
unpack your tent and give the rainfly, tent bottom, and (if you bought one - which you should) the footprint plenty of surface area to dry out.
Next, if you have time, I like to pitch the inner only and then give the floor a good vacuum. They always seem to get leaves, dirt and bugs inside the tent. You will need to use the brush attachment otherwise the vacuum will suck up the tent floor.
Check the tent for any damage in the mesh or solid surfaces and repair as needed. If they are starting to flake around the seam taping then you need to remove the seam taping and seam seal the tent. You would ne d SeamGrip for PU tents or SeamGrip SIL for SilPoly/silnylon tents.
Over time the DWR (usually silicone on higher end tents and PU on lower end tents) fails to properly water proof the point