Washing: A wash is usually a thinned mixture of dark paints used to simulate darkened portions of objects supposedly due to accumulation of dirt, grease etc.on recessed areas, folds and corners. Usually we use dark paints thinned on approximately 10%:90% ratio or thinner. After painting your model, you apply a coat of clear gloss paint to it prior to applying the wash (or you may opt not to, like me). Apply a the thinned solution on your model concentrating on the recessed portions or areas likely to accumulate dirt, grease, etc. Allow the wash to settle on these areas while you can remove the excess on the other portions by wiping it off with a clean cloth or cotton swabs. Let dry and apply another wash if necessary. A wash is already considered one way of weathering.
Drybrushing: After you apply the wash some areas where the wash has been applied would appear to have no details or have a monotone color. To highlight the details especially the protruding portions, you can do drybrushing. It is a method of applying a very thin and almost dry coat of paint (with color a step lighter than the original color of the model) to the protruding parts to highlight them. Get a paint a step lighter than that of the model. Get a stiff brush. Dip the brush on the paint and brush it against a piece of cloth or paper to a point when almost very minimal paint remains on the brush. Now brush it on the protruding portions of the model you want to highlight. Repeat as necessary.
A lot of threads on weathering wash and drybrushing can be found here. Just do a little checking.
Good luck.