Take your time and be very thorough with this step. Also, take a cotton swab dabbed in some rubbing alcohol and go over the internal case components to get them very clean. You can go over the external case with a rag and a little bit of water. Allow your system 2 hours to dry out before turning it back on.
Take care not to drop the processor or pull it off if it’s stuck. Dropping the processor will likely damage it. Alternatively, it may be stuck to the heat sink by thermal paste. Try to separate them. A credit card-type card can be useful for this step, but don’t damage the CPU trying to pry them apart.
Once your PC is put back together, plug it in and test it out.