Limbs have health independent of the creature you're fighting. You can see this health in VATS - just above the percentage chance to hit, there is a bar that decreases as you do damage to a particular body part. (You can see that on this screenshot which is hosted on Wikipedia)
You can cripple limbs by completely emptying this bar before killing an enemy. There are weapons that do bonus limb damage as well as ones that do primarily limb damage that can help with this. Weapons also have a similar bar, and this represents their condition.
The tricky part can sometimes be doing this before you kill an enemy - doing damage to a limb also does overall health damage, so if you do too much overall damage without completely damaging a limb, the creature will die rather than become crippled. On the other hand, if you manage to hit a limb hard enough and cripple it while killing the enemy, you'll often get a rather gory dismemberment or similar result.
However, there's not much benefit to crippling things without killing them - typically the only reason you'd want to try to cripple is if you're facing off against a tough enemy and you need an advantage. For instance, crippling an enemy's legs will allow you to kite it easier, or get away if you can't kill it, while crippling an enemy's arm will cause them to drop any weapons they are holding in that arm.