Think "collage" when you think "collagraph" and you've got the key to this style of printmaking. A collagraph is a print made from a plate that's built up from anything you can stick down onto a base of cardboard or wood. (The word comes from the French colle, meaning to stick or glue.) The materials you use to create your collagraph plate create textures and shapes, while how you ink the plate adds tone to the print.
A collagraph can be printed as a relief (inking the top surfaces only) or intaglio (inking the recesses) or a combination. The method you use will influence what you use to create your collagraph as intaglio printing requires far more pressure. If something squashes under pressure, the result can be quite different to what you expected!
Once you've glued down the collage, seal it with varnish (or sealant, lacquer, shellac), unless you're only doing a few prints. Ideally seal it on the front and the back, especially if it's on cardboard. This stops the cardboard from getting soggy when you're doing multiple prints.
If you're printing a collagraph without a press, be sure to place a scrap bit of clean paper and a layer of newsprint (or fabric/piece of foam) over the piece of paper you place on the plate to protect it. Then apply even pressure to make the print -- an easy way it is to place the "sandwich" on the floor, then use your body weight by standing on it.
When you're new to collagraphs, it's worth making notes on one print of what you'd used, to build up a record of what results you get from what. You may think you'll always remember, but it's unlikely.
The American artist Glen Alps is often credited with coining the term "collagraph" in the late 1950s, but it's not easy to pin down the development of this printmaking technique exactly. There's evidence French sculptor, Pierre Roche (1855-1922), and printmaker Rolf Nesch (1893-1975) experimented with layers on printing plates; that Edmond Casarella (1920-1996) produced prints with collaged cardboard in the late 1940s. By the 1950s collaged cardboard prints were part of the art world, especially in the USA.1
1. The Printmaking Bible, Chronicle Books p368