What do I need to make a bootable external disk?

Question

I got a response from Apple support that said I could make an external disk a bootable one, like a flash drive or ext hard disk, by using an OS X Installer app that was supposed to be available at the Mac App Store.  I looked and couldn't find it.  Since we no longer get a hard-copy of the system install disk, I was trying to figure out what to do to make a 500Gb external disk one I could boot using the MacBook Air with its limited GB storage.
So if anyone can give me the simple solution I'd appreciate it.

Answer 1

Get an external disk drive. Start by partitioning and formatting it:
Drive Partition and Format
1. Open Disk Utility in your Utilities folder.
2. After DU loads select your hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Click on the Partition tab in the DU main window.
3. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the format type to Mac OS Extended (Journaled.) Click on the Apply button and wait until the process has completed.
4. Select the volume you just created (this is the sub-entry under the drive entry) from the left side list. Click on the Erase tab in the DU main window.
5. Set the format type to Mac OS Extended (Journaled.) Click on the Security button, check the button for Zero Data and click on OK to return to the Erase window.
6. Click on the Erase button. The format process can take up to several hours depending upon the drive size.
Next, clone your existing system disk to the external one:
Clone Mavericks, Lion/Mountain Lion using Restore Option of Disk Utility
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
     1. Select Disk Utility from the main menu then press the Continue
         button.
     2. Select the destination volume from the left side list.
     3. Click on the Restore tab in the DU main window.
     4. Select the destination volume from the left side list and drag it
         to the Destination entry field.
     5. Select the source volume from the left side list and drag it to
         the Source entry field.
     6. Double-check you got it right, then click on the Restore button.
Destination means the external backup drive. Source means the internal startup drive.
Test the new clone by:
Boot Using OPTION key:
  1. Restart the computer.
  2. Immediately after the chime press and hold down the
      "OPTION" key.
  3. Release the key when the boot manager appears.
  4. Select the external disk's icon.
  5. Click on the arrow button below the icon.