How to transfer my apps, home, and OS X setup from an external Lion disk to an internal Mountain Lion SSD
The easiest way is to use Migration Assistant, which you can find in /Applications/Utilities/.

It can copy your apps, data and settings from your old disk if it's connected via USB, Firewire or Thunderbolt. You should end up with a mirror image of your old set up.

Start Migration Assistant, select From another Mac, PC, Time Machine backup, or other disk on the first screen, and From a Time Machine backup or other disk on the second screen, then follow the prompts.

If you need more detailed instructions, consult Apple's Migration Assistant Guide (you want the Time Machine or other disk migration section).