How to Install OS X Lion/Mountain Lion from a USB Drive

First you have to purchase it from the App Store.

Locate the the Lion app in the Application Folder (Did notice that I already had it downloaded previously and moved it to my desktop. It actually updated the Lion App on the my desktop and did not show up in my Applications Folder, just an FYI)

Right click and click "Show Package Contents" Go to Contents -> SharedSupport

You'll find a file named "InstallESD.dmg"

Open Disk Utility

Plug in the Thumb Drive. Once it shows up on the left hand side click the Top Level for that thumb drive. You'll know your on the right level if you see the Partition tab on the right hand side.

Click Partitions and select 1 Partition.

Select Mac OS Extended (Journaled) as the Format

You can name it whatever you want.

Click Options -> Select GUID Partition Table

Hit Apply (This will erase anything on the drive)

Click the restore tab

Click the Image button and select the "InstallESD.dmg"

Drag the thumb drive partition on the left to the Destination box. This is the 2nd level down.

Click restore

Once completed, reboot and hold the option key.

Select the thumb drive called Mac OS X

You can let go once you see the Apple Logo

Source: Link OS X 10.7 Lion

How to do it for OS X 10.8 Mountain Lion Link