How to run OS X from DVD or USB stick?
I'm not sure how to make a live environment from a DVD, but it is relatively easy to do it with an USB flash drive or an external HDD.

To install it to your HDD or flash drive do the following:


connect your drive
open the "Disk Utility" and click on the corresponding drive on the left hand side
click on the partition tab and select 1 partition from the drop-down menu
click on options and make sure you'll format it with the GUID Partition Table in order to make the drive bootable

BE VERY SURE ABOUT THIS, YOU'LL ERASE EVERYTHING ON THE HARDDRIVE

now mount your install image and proceed with the installation, be sure to select the proper harddrive


Also, note that you already have a recovery partition.