There are many, many ways to kill someone in Skyrim; you can crush their skull with a war hammer, you can decapitate them with an axe, you can stab them in the back with a dagger, you can hit them in the head with an arrow from half a mile away, you can even slip poison into their pockets and watch them die slowly. Killing NPCs is trickier as you need to do it without being seen, but you can always sneak into their house at night and bludgeon them with a mace.
That said, the best method I’ve found so far? Wait until your target is in the middle of town and hit them with a Rage/Fury/Frenzy spell from somewhere out of sight; they go postal, start attacking people at random and the city guard charge in and put them down for you. They don’t even seem to care when you wander over, loot the corpse and then toss it over some railings into the water.
Why get your hands dirty when you can have someone else do it for you?