Here are tips, plus a bonus, to help YOU take better photos (and the rules apply to video photography, also).
1. Tell a story
Your photo will have the most impact when it tells a story. What are the people doing? What is happening around them?
2. Don't pose (or at least don't let your shot look posed)
Posed pictures are boring. Better to take candid or impromptu photos that feel more spontaneous.
3. Plan your time and place
Often being at the right place and time makes the difference between a boring photo and a powerful one. At events, figure out what the most interesting things are and figure out what the right angle to capture them is. Wait patiently for just the right moment.
For outdoor photographs, time of day can also be important. Early morning and late afternoon light is warmer and less harsh. But also, avoid facing the sun while you shoot. This will increase the odds of ending up with a silhouette (unless that is what you want). It is often still a matter of finding just the right moment.
4. Take lots of shots and choose the best.
"One-and-done" is not the way to get great photographs. Take a photo, look at it, and analyze "how could it be better?" Then take another shot that makes it better. Do this from several different angles, or in ways that capture several different elements of what is going on.
5. Don't center everything in your photo!
This is the biggie, and is a principal you see across many realms of art. It is called the Rule of Thirds. You mentally divide your shot into thirds, both horizontally and vertically. Then you use these lines, in two complimentary ways.
One: The MAIN thing you are depicting should be at one of the intersecting points of those imaginary lines. The rest of the shot should provide balance. Don't put everything right in the middle.
Two: Often, there will be a logical dividing line in a photo. Outdoors, it might be a horizon line, or the edge of a tall building. Indoors, it might be more than one person's face forming a sort of line. Put those actual dividing lines along one of your imaginary thirds lines in a way that provides balance. If people are facing left, put them at the RIGHT vertical line. If you have a horizon line, decide what is more important, the sky or the land and choose your imaginary line accordingly.
Combining these two elements...matching horizontal and vertical lines in your shot with the imaginary lines of thirds, and putting your prime subject at an intersection of the lines...will give you strong, memorable photos.
6. Bonus: For cameras that are not in smartphones -- explore the menus and learn the settings, such as the various focus and exposure options. Often the fully automated mode will not produce the best photos for advanced photographers.
There is a lot more to being a great photographer, but these 5+1 tips (rules) will help you stay on the right track.