Hero units are created by specifying their first and last name in the barracks "Customize" screen. Once you do this, your soldier will be replaced by the hero unit. These units are considered to be cheats, though, as they are super-powered. They have high stats and start with advanced gear. You will be notified when you specify a hero's name that achievements are disabled as a result.
Also note that customization of these heroes is disabled - you can't change their names or any of the other options on that menu (armor color, armor type, gender, etc). You can also take their gear, but your other soldiers can't use it without doing the appropriate research.
You can summon as many clones of each hero as you choose. If you want to field a team of all Sid Meier clones, you are free to do so.
There are four confirmed heroes so far:
(I'm providing their nicknames for flavor, you don't have to specify them when you customize your character.)
These names are given in the game's files, you can find them in:
Search this file for "SuperSoldierFirstNames" and you'll come across all four, in addition to the strings that prompt you when you enter their name.
Here's Otto, note his 100 HP, Will, and Aim:
Kotaku also has a video guide which shows off summoning Sid himself, as well as Ken Levine.