Dry mounting usually refers to heat-activated mounting. A sheet of pure adhesive (no backing) is placed between the photo and the mounting board. Then heat and pressure are applied to melt the sheet and affix the photo. Photos are usually "tacked" in position first with a small "tacking iron". Many dry mounting sheets allow for release or repositioning when reheated.
There are many dry mounting sheets that are considered archival. Many variables such as melting temperature and release characteristics need to be taken into consideration when choosing a dry mounting tissue.
The primary expense with dry mounting is the press. There are fairly serious pieces of equipment since they need to produce both heat and pressure. Differences in models include size of "platen" (the actual mounting surface), available pressure, and the variability and reliability of the heat source. Smaller presses can be used for larger mounting by doing sections. You'll also need a tacking iron, a cooling weight (must be larger than your largest photo), protective release sheets (prevents sticking and marring of the photo) and other less expensive items.
There are sheets and sprays that don't require heat. These are generally referred to as "cold mounting". I've personally had very bad luck with these systems, but they do have their fans.
It's been quite some time since I've been involved in this area, but "Seal" used to be one of the best brandnames for dry mounting presses and materials.
As usual, Light Impressions
is a good source for materials today.