This seems like something that should have been introduced in the game at some point. Granted, it seems like a completely pointless feature (long animation, same result), but I'd like to know for the challenges/commendations anyway.
I originally assumed it was a randomly selected animation when performing a melee from behind, but other people assassinate me 100% of the time in those cases, and occasionally from in front of me while I'm shooting/swinging at them. On the contrary, I've done it myself I think twice ever (one king execution and one assassination with an oddball, which might just be automatic). At this point I'm pretty sure I'm missing something...
In the modern world, "common sense" is an oxymoron.
Assassinations just seem to come to me.. I don't really have a method to getting so many.. I just do.
Mobility, I guess is the ultimate attachment to assist with assassinating. They can sprint as well, sure. But if they need to keep taking breaks from the sprint, you catch up rather quickly.
I also tend to use Promethean Vison, or active camo. Both of those (I guess) would assist in assassinations.
There isn't really a method to it, you just need to see your chances for one. I usually get 2-3/game. Personally, it's one of my favorite things in the game. There's something just so satisfying about slamming a knife in someone's skull that I find.. pleasing.