How do i exactly do a finishing move? I see in videos people go behind a npg and kill him with one strike.

it dosnt always happen in 3rd person i've had a few in 1st person but they do seem to happen at random

It's totally random and can be in third or first person - it's random and is not connected in which person you use for playing. I have also noticed that at least with two-handed-weapons there's a bigger chance to do finishing move if you kill enemy with powerattack.