That sounds overly simplistic, I know. Taking better pictures can't possibly be a two step process. When you consider everything that goes into taking a good picture, learning your equipment, learning composition, learning how to use natural and artificial light and knowing when to use which, learning how to pose a person, or even what moment that candid shot is going to look best, there's no way a 2 step process can do it all. But go with me for a minute... All of the stuff mentioned matters, but really the most important part in my humble little opinion can be done in 2 steps.
Step 1: Take more pictures.
I take a lot of photos. In fact, I would even be willing to boast that I take more bad photos than most of you even to this day. I'd always been interested in photography, had even taken some college photography courses in my early 20's. I'd developed a bit of an eye and considered myself an OK photographer. And I stayed an OK photographer for years. It wasn't until a few years ago that that changed. The biggest change, I started taking more pictures. I carried my camera with me to more and more places, and photographed more and more things. The vast majority of the photos I made were no good, but every time I picked up the camera something was happening, practice. If I couldn't get the picture I wanted, I'd keep practicing. I don't want to tell you how long it took me to get a picture of the moon. I learned several ways NOT to photograph the moon, and I had a whole laundry list of ways of doing it that didn't work, but once I figured it out it was like magic. So nothing crazy here, to get better at anything you just practice practice practice.
Step 2: Show less photos.
You may say, "but wait, didn't you just say to take more pictures?" You're damned skippy I did. Remember when I boasted about taking more bad pictures than you? I mean that, I really do. The only reason I have a reputation of being an even competent photographer is because I showcase only my best work. I was looking at my uncle David's pictures from a recent trip to Africa and WOW, there were pictures in there that I have to admit were better than I've taken. I'm looking at his pictures and I felt like a fraud for even considering myself worthy of being considered good enough to do this for a living. The only reason David isn't considered the premier photographer in the family is because along with a few spectacular images, there are twice as many really good images, even more good images, and quite a few decent ones. When you're done looking at the images you remember it as a really good slide show. Had he kept it to 5-10 breathtaking images I would have gave up my dreams and resigned myself as a hack, but all the other images allowed the viewer a chance to catch their breath. Your less than best images don't add to the best, they dilute the work and end up taking away instead. A Nat Geo photographer may take 20,000 to 60,000 images on an assignment and only maybe a dozen will ever get published. So when you're deciding what images to show to the world, remember that perfection is not achieved when there is nothing left to add, but when there is nothing left to take away.
So there you have it, 2 easy steps to taking better pictures. You don't need a better camera, you don't need more gear. You just take a lot of photos and only show the best of them. Work on those and a lot of other steps will take care of themselves.
Now to repair the relationship with uncle David. I just want you to know that if anything I said about your pictures sounded negative, it came from a place of pure jealousy. I mean, seriously, WOW those were some good pictures. I think I need to go practice.