We learn to appreciate paintings by practicing often, by looking at painting after painting.
There are many places to look at paintings. Online, where there are millions of images of paintings from the masters to amateurs. Books, often with detailed analysis of renowned paintings throughout art history. While looking at paintings from screens and papers are a convenient and efficient way of looking at many paintings, the sense of size and texture are often lost in the process.
The most ideal way to look at paintings is face to face. Grab any opportunity you have to look at any painting on the wall; in exhibitions, art galleries, hotel lobbies, living rooms, art studios, art fairs. Looking at paintings on the wall gives us a perspective of the size of the painting, allows us to look closely at the texture of the painting, and enables us to absorb into the reality of the physical painting that is not merely an image.
How to appreciate paintings? Look at as many paintings as you can, whether online, in books or preferably on the wall.