How to allow write permissions to mounted partitions...

Open up "/etc/fstab" in your favorite text editor, and add or edit the mounted partition line to be:

/dev/hda1 /mnt/dos1 vfat users,owner,rw,noauto 0 0

Meanings:
/dev/hda1 = hard drive partition
/mnt/dos1 = mount point where you want the disk mounted
vfat = filesystem type
users,owner,rw,noauto = options to mount

users => allow users to mount
owner => allow device owner to mount
rw => read and write permissions
noauto => do not mount at boot (otherwise will mount as root)
0 0 => backup option (to dump, don't dump) and fsck option (don't fsck)

Once you do this, any user can do:

$ mount /mnt/dos1

... and this will mount the filesystem.

Check the man on "fstab" and "mount" for more help.

If you want to get deeper into administration, you could set up an
automounter.

See:
Automount mini-Howto at TLDP.org