I have all my plants in pots with holes on the bottom which are then placed inside nicer looking pots that do not have drainage holes. I remove the pots from the covering pots and then I'm free to rince the plants clean. If you cannot remove the plant from a pot that has no drainage holes then you have to be really carefull not to overwater the plants, either use water very sparingly or try to rince only the foliage.
I clean up the covering pots while the plants are drying out a bit. It's amazing how much dirt can be found from the bottom of the pots.
You should notice though that not all plants can be rinsed like this, for example Saitpaulia that has hairy leaves, does not like to have water on the leaves. I have no idea how that type of plant has ever survived in the wild, but that is what all the plant guides say.