In order for a user to have read/write and execute priviledges, they need a chmod of 7, this correlates to a umask of 0. So if you want not only your user, but all users in a group, the owner, and all other users to have read/write and execute permissions on any given file/directory then you need to apply a umask of 000. Sounds confusing doesn't it? It's not, but you have to understand umask and chmod first. Check out the man page on those 2 things. For a "quick start" though, find the line in your /etc/fstab file corresponding to this fat32 partition and locate the "defaults" entry. Now change it to look something like:
/dev/hdb6 /mnt/fat32 vfat umask=000,auto,users,rw 1 0
Changing the partition and mount points to suit your needs.