The easiest thing would be to stop mysql, move the files to the new folder and make a symlink from the default to the new folder.
If it's a separate drive you can just change the mount point to the default location as well:
Filesystem 1K-blocks Used Available Use% Mounted on
/dev/cciss/c0d0p2 10154020 1518184 8111716 16% /
/dev/cciss/c0d0p1 101086 15310 80557 16% /boot
tmpfs 1037808 0 1037808 0% /dev/shm
/dev/cciss/c0d0p5 122510780 43692600 72494596 38% /var/lib/mysql
EDIT: Here's the line from my /etc/fstab
LABEL=/var/lib/mysql /var/lib/mysql ext3 defaults,noatime,nodiratime 1 2
You shouldn't have any trouble updating the packages either mounting at the default location, using links or changing the location in the my.cnf file.
EDIT: Here are the items that you would edit in your my.cnf:
#basedir = /var/lib/mysql
#datadir = /var/lib/mysql/data/