There are two ways you can add fiberfill. The bunches of the stuff like you find in pillows, you simply pack in loosely. 1LB of fiberfill per cubic foot of space in the woofer is usually the rule of thumb for filling it. Or you can add it a 1/2LB at a time until you like the results you're hearing. Either way, between the "rigidity" of the fibers (for lack of a better term) and the amount you'll end up adding, it's not going to really move around or settle to the bottom. The alternative is lining the box with fiberfill batting, which is more consistent like a fabric, though it's the exact same material, just "woven" more tightly. This will keep it away from the driver and look a little neater - not that you're going to be seeing it again, but some people are anal retentive about these things.
If you decide to go with the loose stuff, using a bit of netting or fabric to keep it away from the driver, just in case, is a good idea as well, as previously mentioned. And definitely make sure it's fire re.tardant.