From the manual:
Backing Up The Database via SSH/Telnet or
Backing Up The Database via phpMyAdmin
Restoring The Database via SSH/Telnet or
Restoring The Database via phpMyAdmin
If you don't have shell access, some people have also reported success with these scripts:
MySQLDumper
MySQLHotxcopy
Bigdump
There are also a few scripts in the modifications area to help you out if you want to go that route.