How do you do a complete reinstall of Lion?

Restart holding the Command + R keys, that takes you to the Recovery HD...follow the on-screen guidance to reinstall.

Instructions are in thisknowledge base article.

Install or Reinstall Lion from Scratch

If possible backup your files to an external drive or second internal drive.

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.

Erase the hard drive:

1. Select Disk Utility from the main menu and click on the Continue button.
2. After DU loads select your startup volume (usually Macintosh HD) from the left side list. Click on the Erase tab in the DU main window.
3. Set the format type to Mac OS Extended (Journaled.) Click on the Erase button and wait until the process has completed.
4. Quit DU and return to the main menu.

Reinstall Lion: Select Reinstall Lion and click on the Install button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.

Restart the computer into recovery mode. You will have four options. One of which will be to reinstall your software.