Forest origins can be narrowed by looking for shade-intolerant pioneer species. These include trees like Birch and Aspen. Remember that old growth forests have a great deal of diversity. Thus, presence of these pioneer species can indicate that the forest was cleared in the past.
Stumps left behind after logging can be found up to a century after they were cut. Large conifer stumps can last in a forest for well past a hundred years, especially in dry conditions. By intuition, all stumps should have a tree next to them on the ground. Look for a down tree or even just a moss trail, which could be all that is left of the log. With no signs of a remaining log, one can be quite certain that the area was cleared and had it's timber hauld off.
There aren't many better signs of old growth than an abundance of large logs in different stages of decay. This also includes trees that are dead but still standing. This simply shows a long history of being left alone.
Observing the width and height of forest trees is a great way to wrap your head around the history of the forest. For instance, a forest with a very tall canopy and wide trees is typically very old. The height of these trees often signifies the extent to which they have had to compete to get there. This typically means less availibility of light and nutrients, slowing the growth of the trees. Thus, most old growth forests will have exceedingly tall canopies.