Make sure your hands are clean before you start, and if they pick up dirt in the process, be careful not to re-apply that dirt to the model.
Start by picking up the model and tipping it over so most of the dust falls off. Gently shake and tap the model to loosen up the dust and encourage it to fall off.
Then gently blow on it to further remove the loose dust. You can blow on it using just your mouth, or you can use canned air (available at computer supply stores) or a blower bulb (from a photography supply store). Practice against your hand to make sure you're blowing only air, without any spit. You can use a straw to concentrate your air stream and direct it exactly where you want it. Before using canned air or a blower bulb on your model, practice against your hand until you know how far away to hold the can or bulb to get an air stream that won't damage the model.
Use a soft brush (like a paintbrush) to dust out crevices and clean the stickier dust off of surfaces. You might want several different sizes of paintbrush - larger ones for cleaning larger, nearly flat areas, and smaller brushes for cleaning out tiny details.
If your model has a water-resistant coating, use a damp cloth to wipe off any stubborn dirt patches.
A protective coating will also make your model sturdier, so you're less likely to damage it when you handle it for cleaning. According to Wikipedia, people often use varnish or resin as a coating for pepakura models. You can also fill a model with spray foam to make it more durable.