You can get the different stealth kills by being in the correct position in relation to the enemy.

Easy stealth kills
Sneak up from behind.

Sneak up from behind and crouch.

Jump on enemy, while pressing Attack in mid-air.

Moderate stealth kills
Sneak from the side.

Hard stealth kills
Sneak from front (or wait for them to turn around into you). This must be timed perfectly.