I have two friends who are retired photography teachers and I still see
my old teacher around town. My old HS physics teacher's wife teaches photography and I've talked to her a couple times. One thing they will all agree upon is that viewing lots of photos is a very good way to understand what makes a good photo.
I think it's like muscle memory of the eye. Rules of composition are a good baseline for someone who is still figuring it out or is totally OCD but the truth is, not all good photos adhere to these rules.
Look at photos every day. You'll know a good one when you see it. After a while, your brain starts to see good photos all around you. Then, point the camera at it and capture it. To me, perspective and light > composition. You still need a subject though.
If you want to teach yourself to use the rules of composition, I think practising abstracts and still lives would get both halves of your brain around it.
Edit: S2 and S5 pro.
That's why I post either B&W film or jpegs form my droid here.