How do you watch your games after you play, and what do you use to do it?

So...I love the game...sadly I'm an old fart working the grind etc so I do not have tons of time to play and tackle getting better via brute force methodology. I hear a lot of people talking about watching their games after and anazlyzing what they're doing wrong. I'm curious how this is accomplished? What pieces of software do people use to record their matches and view them again?

Additionally....does this work only from the perspective of the character you're playing...aka...do you record your game and only get the vantage point that you saw during the time you played. Or...does some of the recording software actually manage to record the game from an overall perspective like what you can see when you spectate a match?

I'm not overly good...I was Silver last season...and I imagine when I play my provisionals I'll probably be in Bronze simply because it seems most people are dropping a rank at the beginning..so'k...I don't mind. My goal is to eventually climb to gold...which I think would be a worthwhile accomplishment for a guy in his 40s. So, because I only have time to play maybe 4-6 games a week I think it would be worthwhile to slowly improve my play by being able to rewatch my work and understanding what I did wrong. My mechanics are so so, but I have excellent game knowledge...I just tend to tunnel vision while in game and lose the advantages my knowledge should bring. I think viewing my game play could greatly help that.

TLDR: What do you use to view your matches after they're finished so that you can learn to spot your mistakes and how does it work?