There are two good ways to remove loose dust from models, brushes and compressed air. A dry, soft-haired brush works best for gently removing dust from a model without damaging delicate details. Brush lightly, working from top to bottom. Be particularly careful around details and electrical contacts.
For getting into tight places, compressed air is a modeler's friend. You can use canned air cleaning products designed for electronics, or an airbrush. In addition to cutting costs, an airbrush allows you to regulate the pressure. Start low and work up. Air is a good alternative for getting dust out of trucks, running gear and other areas with moving parts.
For stuck-on dirt and grime, you're going to need more than just a dry brush. Use liquid cleaners very sparingly on models. Some chemicals can attack paint, decals, even plastic. Museums generally use an extremely mild (1%) solution of soap and water to clean artifacts. The same will work on models.
Apply a mild soap wash with a cloth or towel that is lightly damp. Work slowly and cautiously until you find the pressure and moisture necessary to remove the dirt and only the dirt.
Cotton bud sticks work well and make sure not to use a soap that is 'Gentle on Hands' it will put more residue on your project. These are tighter wound and won't leave lint behind like Q-tips.
Wheels and Electrical Pickups
Dust and grime on the piece may ruin a model's appearance, but the same dirt can destroy its operation if it coats the electrical contacts. Left unchecked long enough, dirt build-up on wheels can even cause a derailment.
For normal cleaning, soaking a paper towel in liquid cleaner works well. Place the towel on a track and drag cars back and forth, pressing down lightly. For locomotives, clean one truck at a time, keeping the other truck off the towel on the tracks for electrical pick-up. To clean while you play, try some of these easy-to-make passive wheel cleaners.
For heavy dirt build-up on wheels, a small flat-head screwdriver or hobby knife can be used to gently peel off the grime.
Don't forget electrical contacts inside the trucks as well. It may be necessary to partially disassemble the trucks to get to the contacts. Clean the backs of wheels and the metal contacts gently with liquid cleaner. Blow any dust out of gearboxes and wheels as well.
While you've got the trucks apart to clean wheels and contacts, take one more moment to re-lubricate. A small drop of light oil in the journals on freight and passenger cars, and a compatible grease in gearboxes will reduce friction and noise. A little is all you need.