Leave the white stuff -- that's the wick that holds the juice and keeps it against the atomizer.
If you need a quick fix, just drip one drop of the liquid onto the white stuff, wait for it to soak in, and then another drop, let it soak in, and so on, until it starts to look saturated (the drops aren't disappearing, just kind of sitting there. I don't know how big your cartridge is, but if it's roughly the size of a cigarette filter (like my 510), you should be able to get at least 10 drops in (you don't have to use that many, you can do 5 drops and puff for a while).
Then plug the cart into the atty, and you're good to go.
If you want to make it easier to add liquid, think about the "straw mod" (do a Search on "straw") or PTB (Pyramid Tea Bag) mod (do a Search on "pyramid"). Either way will let you drip the liquid in more quickly and get more in before it stops being absorbed.