It's very simple. To dry sautée, simply add your cleaned mushrooms or other watery food to a hot pan that has nothing in it; no oil, no butter, no water, no spices. Nothing. The heat will release the liquids from the foods and they will brown and get a really nice texture. Stir often to prevent burning and cook until the natural juices have evaporated. You should do this over medium high heat.
Dry sautéeeing wild mushrooms is also a good way to remove excess liquid so that they will freeze better.
(Image: Kathryn Hill)