This is a really far-reaching query. Weathering covers a ton of ground, from simple dust to mud encrustations, water streaks, chips in the paint (just to to primer, or exposing metal), rust/corrosion, oil stains, general grime and dirtiness.
Unfortunately it\'s hard to get away from airbrushing being an excellent way to get certain effects on vehicles (things that are very hard or even impossible to do by brush). You can get close using certain techniques but they\'re not exactly the same.
So, dust? If you can\'t get MIG powders or you can\'t afford them you can get pastels from any art shop and if you scrape them down you get a fine powder that can be applied for some great dust effects. Pastel dust can also be applied wet (with water or turps/mineral spirit). A good dust effect can also be achieved simply with careful washes and thin layering of very dilute paint of the right colours, although it\'s harder to predict how things will look when the paint is dry; adding in a little talc to your paints for this can be useful
Chips? Assuming the vehicle is already in the base colour you just paint the chips in very carefully with a fine brush (primer colour / dark grey or grey-brown for exposed but oxidised metal / rust colour for an old chip / bright metallic for freshly-exposed metal) then, if you like, you can paint a fine highlight line on the bottom edges of the chips and a fine shadow line on the upper edge of the chips.
Mud? You can make a great muddy slurry with fine sand, paint and a dot of glue. This can be applied with any tools or just an old brush. You can paint it further - highlight, add a bit of shadowing - when it\'s dried if necessary (although it often looks really realistic as-is).
Rust stains? Mix appropriate rust colour, apply with a fine brush in vertical streaks from scratches, bolt heads, shot damage etc. Pooled rust stains can be applied simply as spot washes. Heavy rusting can be simulated nicely by mixing in some talc or fine sand into the paint, maybe stippling it on.
Oil stains? Mix glossy black or black/brown colour, apply where needed in streams, pools etc.
Wear on edges? Simply running a hard graphic pencil over areas of high wear can achieve a lovely worn-through-to-metal effect. I would generally recommend you grime up the model pretty much fully before you do this.
Einion
