The good old finishing moves have made a return in the new Call of Duty: Modern Warfare game, but some players seem to have some issues with actually using them. You are required to use these in multiplayer games if you want to unlock all Operators, so don't neglect using them,
Using a finishing move is very easy, and all you need to do is hold down the melee button when you are in range of an enemy. The finishing moves only works on unaware enemies, for they can for example be useful against campers if you sneak up behind them. So hold down the melee button, which is R3 on Xbox One and PS4, or mouse button 5 or E on PC, depending on your set-up.
If you just tap it like you usually do, you simply get a melee kill, and not an execution / finishing move.
And that's all there is to using a finishing move in Call of Duty: Modern Warfare.