Steelgohst has it down. If I had to make an addition, I'd say that with dark colors and materials, my favorite way show wear by physical defects and deformities.
Light colors show age primarily through the surface finish, as that is what our eyes see first. Something we expect to be white or brightly colored, when tarnished, causes us to notice the differences between our mental expectation, and what we actually see.
So for dark colors, which mask surface discoloration effectively, I would suggest more of a physical approach. Take the fabric outside, rub it in some dry earth, wrap it around a tree and whack it with a mallet... so on and so forth. Tiny frayed ends and scuffs (no giant rips as you requested) go very far to suggest the age of a dark cloak or shirt.
Notice these dark jeans. The most dominant feature on them is the creasing where the fabric looks physically displaced. A plain black t-shirt can go from Johnny Bravo to Mad Max really quick if its beat to hell.
But above all, as was said, don't think about it too much. If your character has been in battle, take that shirt and battle it into submission.