Yes, there's actually something else in this world that you need to clean. But this part is much more fun than laundry or bathrooms.
Dump any remaining soil out of the plant pot. Run water into the pot and scrub the sides with a scrub brush to remove dirt build up and white mineral scale. The mineral scale can be stubborn so chip it off with a butter knife if necessary. Apply a few drops of liquid dish detergent to a scrubber sponge and clean the inside and outside of the pot. Remove the drainage tray and scrub that too. Don't forget the bottom of the pot.
Rinse the pot thoroughly until all soap residue disappears. You're now ready to plant!