Appalachian Trail Data Book
I've noted the miles hiked for several pictures. There is only one 'mile marker' on Trail that I recall, up in New England. There are some signs along the way, such as the side trails to shelter camping areas (blue blazed trails), at some trail head parking areas near road crossings, or with junctions of other hiking trails, signs may note distances.
For most of the trail, we have to rely on publications. The ATC sells a pocket-sized Data Book with all of the mileage data tabulated. It is a paperback, so I carried mine in a ziploc bag, tucked in a readily reachable side pouch of my pack or in a cargo pocket of my long pants.