Photography is an interesting skill to level. Prompto will randomly take pictures while you are doing stuff and each time you sleep you will get the chance to look through them. There also appear to be 150 camera locations across the map where you can physically trigger a picture to be taken. It seems that you can get this to max while just playing the game however going to the 150 locations on the map will get it for you faster!
There appears to be no benefit from saving or sharing the pictures you take other than just having them to look at again or showing them off to friends.