Just want to say I'm still learning when it comes to the painting department, and if you have an artist on hand to teach you, I would suggest asking them for help. Not doing it outright for you, but definitely showing you their own techniques. That's how I've learned how to cosplay thus far.
Enough of the soapbox lol.
As I said I'm not particularly good at painting, but I usually paint all the way to the base colors that I want then I take a weathering color (typically black, but sometimes yellows, browns, and oranges depending on what I'm weathering) in acrylic, putting it onto a paper towel then wiping it onto the piece. Don't let it dry, immediately wipe off the excess and leave a "residue" on it.
I've also done a method called "dry brushing" where you have small amounts of paint on the brush then lightly feather paint onto the piece, but I haven't had much success with large pieces of geometry using that method.
Here is what I think is my most successful paintjob, and I used that paper towel method I was talking about, all in blacks.