An example for an init script can be found at /etc/init.d/skeleton in most distributions.
As for the snapshot, create it first from the shell and modify /etc/fstab to boot from the snapshot instead of the usual partition. Then, in the init script, make sure that all required modules are loaded, remove the old snapshot using lvremove, and create it new, using the same command as on the command line.
A good intro to LVM can be found at The Linux Documentation Project