So a lot of times when you melee, either with your gun or another weapon, your character will tackle or do a leg sweep or whatever. I've tried googling it and people say to press Alt twice (not sure what it is on consoles) or they say that it's random or they say it's a finishing move when they're low on health. The double tap alt thing doesn't work. Sometimes you'll do a special move, but sometimes you'll do a special move also when you only press it once -- so that's completely irrelevant and purely coincidental.
I discovered how to do a sweep/push move -- aim at their legs and press Alt. I've only tested this in third person, but every single time I aim at an enemy's legs and press alt, I would do a leg sweep or I would push them. I've been able to replicate this 99.9% of the time. Just aim at their legs, press alt, and you would do a sweep/push move no matter if you're using a gun or melee weapon.
As far as the other moves where you tackle them and punch them, I'm not sure. There are times when I've pressed alt right as a melee enemy was about to attack me and I would do a counter attack, so maybe that's one of them.
Sorry if you guys already know this, but I haven't seen a thread about it. Just thought I'd share.