I think executing a person is when you're close enough to them to trigger the auto animation, making John shoot them close up or slice their throat. I'm surprised you're almost through the game and haven't gotten 20 though. I usually performed them by mistake. (An example of an execution animation is when a quick cutscene plays when John puts his rifle underneath a guy's chin and blasts a hole through his head.)
No problem, oh and for a way of getting the executions easily, other then shooting at close range and hoping to trigger it, is to lasso people up and knife them. All you have to do is crouch down by them and use your knife command. I think that auto triggers the slicing throat execution every time.
Another way that works well is to walk around Casa Madrugada with the Throwing Knives out and walk up to someone from behind and push RT without aiming. No Rebels or Army in Casa Madrugada, so you shouldn't get in trouble with the law either. Hope this helps.
What's a Kraken gonna do to you? Somehow through the trials of the day/I come out on the other side with the chance to say/ hey baby, are you doing okay?
Shoot them in both knees, once each, with the Cattleman Revolver. Walk forward as they are getting up, hit RT with your weapon of choice out and witness the most gruesome execution animation, IMO. Also works from behind.
Wake me up before ya go go! :D http://www.youtube.com/watch?v=LSd_kgDkVTE