Buggs described a good method.
What Ive had success with, if the carto is not too flooded yet, is to remove the tank and remove any excess juice from the battery's connector, and blow any juice from the cartomizer into a paper towel as Buggs described.
Then I'll put the tank back on the battery. I'll then do some pre-burn puffs. I'll power on the battery for about 2 seconds to allow the excess juice vaporize in the carto, then vape it gently. I'll repeat this a few times until it is vaping the way I want it to. This method limits the amount of additional juice that will enter the carto while attempting to vaporize what is already in it.