As noted in the Vocabulary section, dry mounting is used when one wishes to laminate something to a surface (the "substrate"): wood, a different kind of paper, etc.: in short, when one is attaching a document to something else, usually for display purposes.
The machines to do this are sometimes referred to as presses, since that's the way they work. They require a special film, called a tissue; this is heated to a specific temperature, applied with a specific pressure, for a specified time. The items are placed together in a "sandwich" composed (from top to bottom) of a release, the tissue, the document, and the substrate. (The "release" is a peel-away sheet of some material, which makes sure that the tissue doesn't stick to the heating/pressure plate, which can easily be peeled off the tissue once the operation is complete). The mechanism is heated and engaged, the pressure is applied, and the results examined. If the mounting is unsatisfactory, it can be repeated with the same material package, or can be started all over.
An alternative to the process using heat-activated adhesive described above is the pressure-activated adhesive process. Coated papers applied to coated substrates don't do as well with heat-activated adhesives. However, for most other cases, heat-activated adhesives are preferable, being cheaper, easier to use, allowing more flexibility in one-pass mounting-laminating applications, and are less tacky at room temperatures. Pressure-activated adhesives will adhere to a greater range of materials and allow for pre-coated backboards.
Dry mounting is a rather specialized laminating application so unless you're going into it in a big way, it's certainly better to have any such work done by a service bureau.