Download an OS X installer

How to save an OS X installer from the App store and create a bootable Flash drive:

After purchasing and downloading OS X from the App Store, the installation program will automatically start. Instead of completing the installation immediately, quit the installer and make a copy of the OS X installer (copy it from the Applications folder to your Downloads folder). It is critical to copy the file before completing the install as otherwise the installer will delete itself automatically.

To copy the installer onto a bootable USB flash drive, prepare a blank (8 GB+) USB drive as follows:

Open Applications | Utilities | Disk Utility
After DiskUtility loads, select the flash drive (the entry on the left with the ID and size). Click the [Partition] tab in the DiskUtility main window.
Under the Volume Scheme heading, set the number of partitions from the drop down menu to one. Set the format type to Mac OS Extended (Journaled.)
Click the Options button, and set the partition scheme to GUID and press [Apply].
Now locate the saved OS X installer in your Downloads folder. CTRL- or Right-Click on the installer and select 'Show Package Contents'. Navigate to Contents/SharedSupport. In this folder you will see a disc image named InstallESD.dmg double-click on this to mount it.
Open Disk Utility, select your empty USB flash drive from the left side list and click on the [Restore] tab, choose the InstallESD.dmg file as the source and your USB flash drive as the destination. You can drag and drop the USB flash drive volume from the left side list in DiskUtility and drag the mounted disc icon from Finder.
Double-check you got it right, then click on the [Restore] button.

When the clone is completed you have a fully bootable installer that you can use without having to re-download OS X

It is also possible to copy the InstallESD.dmg file without mounting it first, but this may cause the error "Could not restore – Invalid argument" this error can be safely ignored.

This routine has been tested with Lion and Mountain Lion.

Related:

OS X Syntax