I imagine there's a few options:
If it's non-absorbent like a tarp/fly or rain shell, I'd shake it off and just cram it in the top of my pack. All the important stuff is inside the liner with my bag and down sweater.
If I managed to get something wet that soaks up water, like clothes or an insulation layer I'd reconfigure the compression straps to hug all the way around the pack and lash the wet item as spread out as feasible to encourage some sun-drying.
Something small would go in the mesh pocket on the side.