The quick and easy way is to run the hot water in your sink and fill the atomizer over and over and allow the water to drain from the battery end. Do this over and over for a couple of minutes and then blow the atomizer dry. Allow it to sit and drain for 5 minutes, connect a battery to it and dry burn until you can see a cherry red glow. You need to go to a darkened room to do the dry burn so that you can see the glow. Don't dry burn past the cherry red point.
Then, drop 2 or 3 drops of
juice on the webbing in the atomizer, re-insert your cartridge, and vape until you begin to get good vapor. You may have to vape it for a minute or so to get all the water evaporated. Then you will get good vapor and the taste of the previous
juice will be gone. You will also notice that the visible residue of the old
juice is gone and the inside of the atty is bright and shiny after washing.
If you have a local hobby shop, buy a test tube holder. It's a tweezer type device that has curved jaws. It will let you wash the atty under hot water without burning your fingers.