I started scoring in the 70's early in high school. Improved fairly quickly once we joined a decent country club. I was always able to get the clubface to the ball and had a nice draw from the start.
In high school, I spent a lot of time on the putting green learning how to not 3 putt. Learned pace and feel on longer putts. My swing is more of a sweeping motion, so I became pretty proficient at the short iron shots and was really good with a sand wedge from 100-120 yards.
Walked on in college and shot some good scores, just never really was able to make it to the next level.
After college I played some solid rounds in the 60's on easier courses. At that point I started losing my nerve on the greens and lost confidence. Have just played for fun since.
I still generally shoot in the 70's. Looking back at my peak, I feel that length was the most valuable part of my game. I could hit a wedge 150 yards and my driver in the 280-300 range. Par 5's were the holes to dominate as well as the short Par 4's. Also, I rarely 3 putted and was able to get up and down the majority of the time.
Nothing worse than a bogey, making 2-3 birdies a round, limiting 3 putts, and trusting your swing and not steering the golf ball is a path to consistently breaking 80.
I would say length off the tee is one of the most important things to shooting low, makes approach shots significantly easier.
I still shoot in the 70's on familiar courses, just notice I tend to give away shots at a higher pace now and my hands are shaky on the greens now. Which makes me laugh at times at how much I miss hit putts now.