Most folks will find that just taking lots of images and looking carefully at them will train their eyes/brain over time. Those who just glance at pix ("cute kitty") and do not really look/think about them may not train their eyes/brain over time.
Personally I recommend that folks pay attention, think, and learn. Digital photography being free means pretty much everyone can readily improve their photography. But it does require some effort.
That's outstanding advice and a great start in training one's eye, learning how to see, thinking about pleasing compositions, learning about different qualities of light, thinking about potential narratives a photo could release in a viewer's mind, etc.
Further along, I would suggest purchasing (a lot of) books of photographs by photographers whose work one admires, and is inspired by.
For me, when I was getting started, and was/is interested in photographing people, it was Robert Frank, Richard Avedon, Dorothea Lange, Manuel Alvarez Bravo, Daido Moriyama, Diane Arbus, Robert Klein, Arnold Newman, Graciela Iturbide, Garry Winogrand, Platon, and more.
For other kinds of photography there will be a similarly large number of well-known photographers to draw inspiration and knowledge from.