Disclaimer: Golf Nola has no affiliation with the USGA. Links and images are for informational purposes only.
First, let me start by saying this is not an overnight improvement, it will take time as you learn the rules, and it is possible you may see higher scores for a short while.
One of the first things you want to do is learn and know the rules. One of the best ways to do that is to purchase a USGA Rules Book every year or get the USGA Rules of Golf Mobile App. When I purchased the Mobile App at the time it was $4.99. I only purchased it one time, in 2015, and it has been updated every year with any new rules changes.
Once you start to know the rules and play by them every round of golf you play you will start to see your scores lower in a few key ways. Playing the ball down, using the rules to your advantage, and holing out on every hole.
Playing The Ball Down: First, it is hard to break a rule if you never touch your golf ball and this is a good habit to be in. Especially if you want to play any competition golf. The second is by not bumping or rolling the ball you are learning to play from different lies. For example, if your ball lands in a dry patch in the fairway, instead of bumping the ball onto the grass you are training yourself to be more precise. When you can play from different lies you can hit better shots from those perfect lies. This is the same for the rough. If you constantly give yourself a good lie you are actually hurting your game and limiting your shot selecting and imagination.
Using The Rules To Your Advantage: The more you know the rules the more you will know how to use them to your advantage. There will always be certain situations that will cost you a stroke but they do not have to cost you two. Take for example an unplayable lie scenario. Many golfers I have played with thought they were only allowed one club relief from where the ball is unplayable, no closer to the hole. One, that is wrong and there are actually three options. 1. You can go play from the spot of your last shot, 2. take the point where your ball is unplayable between you and the hole or go back as far as you like, or 3. take a two club-length relief from where the ball is unplayable no closer to the hole. One thing to always remember when taking relief. If it is free relief it is one club-length relief, and if it involves a penalty stroke it is two club-length relief.
Holing Out On Every Hole: Besides just accurately counting your round of every stroke this helps build confidence and helps your putting game. The more you take gimmies from inside 3ft the less chance you will have to make those when it matters. No, I do not mean you can not make them but when you are not used to putting them it adds to the nerves and sometimes will affect your putting stroke when you have to make them count. I learned this the hard way in 2007 playing on a professional mini-tour. I missed a cut or two by missing a 1ft or 2ft putt. Why? I was used to people I played with giving me those putts and I didn't practice inside putting inside 5ft at the time. The more you make yourself putt those out on the course the more confidence you will have making them.
Those are the main ways playing by the rules of golf can improve your game. This will also come in handy when playing matches against other golfers. If you don't currently play "by the book", so to speak, go give it a try one day and see what happens. You may learn some strengths in your game you didn't know you had or find some weaknesses you need to work on.