I’ve seen many techniques for this. You’ll have to look up the “how” part, but I’ll give you a list of things you could search for, based on a weathering workshop I attended, which was run by a theatre costume company.
Bleach in a spray bottle – you’ll get varied results based on whether you mix it with water, time you let it set before rinsing, whether you rinse or not, etc
Clean dirt – this is an SFX makeup product that is exactly what it says on the tin. It’s real dirt, but without the natural micro-organisms and bacteria present in dirt you pick up off the ground. It’s only permanent if you use a lot and leave it for a while before washing, though. Just like regular dirt, it can be washed away.
Sandpaper
Sand barrel – a barrel or bucket with a lid filled with sand, stick the costume in, and then roll it around, run up and down the street with it, etc
Car – not kidding. Put it on the ground and then run over it a few times with a car. Usually done on heavy fabrics, like canvas, fatigues, etc
Fire – be really careful, but they talked about how the character was supposed to have jumped through a fire or something, so they had to map out where the shirt should be burned, and then literally set it on fire while trying not to burn the entire thing
Tea wash
Dirty water
Last note: A very interesting video I saw in a film costume exhibit showed how the costume department created a frosted effect on a parka for a movie set in Alaska/the arctic. They used melted wax, applied with a paintbrush. Cool eh?
