The best and easiest way is to take warm and soapy water with a sponge to clean all the inside parts of the percolator. Firstly wash the brewing basket and the base of the water chamber, also scrub softly the tube that connects ground coffee and water.
For deep cleaning, you can also use baking soda and vinegar to remove all the stains and residues of coffee. The right time to do the cleaning is after brewing the coffee; in this way, you'll always get the fresh aroma and desired flavour for the next brew.