"nic free is the way to be"....lol.
So you have 2 issues:
1) Cleaning out the old atty
2) Cleaning out the old juice from the cart
1) Rinse the old atty out with water or IS Alcohol (91% or better, pharm grade... not rubbing alcohol with other additives). Blow it out. Dry, with a "warm burn", or air, or time. Like typocinnamongrl said.
2) Clean out the cart. Remove the little sponge filler, rinse it out, and rinse the cart out, dry the filler in a paper towel, and put it back.
Put 3 drops of juice into the atty, and some onto the filler (10 or so on the filler with a 510 cart)
FYI - you can get "blank" unfilled carts. New atties don't have nic, just primer.