Here are some links to useful resources:
Post on ExtremeTech.com
Flash memory HOWTO on ibiblio
Essentially it boils down to adding a line to /etc/fstab and then mounting /dev/sda1 or /dev/sdb1 on some mount point (directory). You don't strictly need to edit /etc/fstab, but if you don't you will need to be root in order to write anything on it. Here's the magic for /etc/fstab to allow non-root to get read/write access:
/dev/sda1 /mnt/usbstick vfat rw,user,noauto 0 0(assuming your mount point is /mnt/usbstick.)
If that doesn't work, check /var/log/messages and see if your stick is on /dev/sdb1 instead.
I'm looking forward to it being as easy to use USB sticks under a default Linux distro as it is under Windows, though. I hate to say it, but under Windows, they "just work."