The quick answer is: you don’t!

You should never attempt to clean the inside of a cartridge. 

NEVER.

Now that we have that out of the way, there are some circumstances where you might like to clean the outside of your cartridge. It is important to make sure the inside contact point of your battery and the contact point of your cartridge are completely clean for the best vaping experience. It is best to use a Q-tip cotton swab and rubbing alcohol to clean these surfaces. Even a very thin film of oil or debris can interrupt the connection point with the cartridge. You can use this same method to remove residue from the exterior of your battery or cartridge as well.