This video explains the process.
You have to capture an enemy first using the Dartgun's secondary fire mode, then carry them to a Rescue Zone (they are purple areas with a label). You can't just exit a level when you do this, you have to beat the Mission. In the main menu, press the "L" key to load a secret level that will make capturing enemies much more convenient (it's the one shown in the video).
After that, go back to the starting area and use the Character Customization terminal where you can customize the characters you just saved.