How do I do a clean install of Mountain Lion with no disc?
For Repairs/Recovery:

One is to use the build in recovery installed on your hard drive. To check for it use disk utility, but it is a hidden partition so make it non hidden first.

Second one is to use the Internet Recovery.

For clean install:

is to create a bootable USB, with complete ML installer. (you need to have/purchase the ML installer package), and a USB with 8GB space. 

http://macs.about.com/od/usingyourmac/qt/How-To-Re-Download-Apps-From-The-Mac-App-Store.htm

Example:

OS X Recovery Disk Assistant v1.0


  The OS X Recovery Disk Assistant lets you create OS X Recovery on an
  external drive that has all of the same capabilities as the built-in
  OS X Recovery: reinstall Lion or later, repair the disk using Disk
  Utility, restore from a Time Machine backup, or browse the web with
  Safari.
  
  Note: In order to create an external OS X  Recovery using the OS X
  Recovery Assistant, the Mac must have an existing Recovery HD.
  
  To create an external OS X Recovery, download the OS X Recovery Disk
  Assistant application. Insert an external drive, launch the OS X 
  Recovery Disk Assistant,  select the drive where you would like to
  install, and follow the on screen instructions.