This article was originally written for the Board Game
Designers' Forum; it's available there as a BGDF wiki article.

Foamboard, sometimes called foamcore, is essentially two thin pieces of plastic or cardboard with a layer of foam bonded between them. It is available in many colors, finishes, and sizes. Notable finishes include self-adhesive backing (like a sticker) and metallic coatings. Most retailers carry sheets measuring roughly 2' by 3'. Thickness varies from millimeters to inches; 3/16" (4mm) is the most commonly available at retail art supply stores.

Foamboard is widely used in modeling, especially in architectural design. Chief among its advantages are widespread availability, sturdyness, longevity, and ease of cutting and folding. Even large sheets will keep from warping for quite some time. Foamboard also generally won't chip, dent, or break as easy as some materials.

For board game designers, foamboard is a great choice as a backing to create boards, tiles, and even chits for prototypes or homebrewed games. In addition to the properties above, it lends a nice weight and feel to these pieces, greatly aiding the appeal of the prototype.

Although relatively easy compared to some materials, working with foamboard does take some care. The following are a few tips:

• Consider using black or dark colored foamboard; this makes it less obvious when a piece is dirtied or otherwise marred. By a similar token, dark colors also help obscure burrs and slightly irregular cuts. In addition to the obvious aesthetic benefits, this makes pieces last longer when it is important to not be able to distinguish them, i.e. from the back. For the most part though, colors and finish should be dictated by the feel of your game. Large, black tiles can certainly be more somber and of a darker mood than white or lightly colored pieces.
• Generally, you will want to print out your artwork and mount it to the foamboard before cutting. Spray adhesive works best for this, providing the most uniform, thin, and long-lasting bond. It is however somewhat tricky to work with, as it has no set time and provides no ability to adjust the print once in place. Rubber cement applied thinly strikes a good balance between making a good, uniform bond and allowing for some adjustment. Note that spray adhesive also requires good ventilation, as the odor is frequently even stronger than spraypaint. Other techniques include a wash of diluted white glue, or printing onto self-adhesive (sticker or label) paper.
• Hobby knives, razors, paper cutters, and rotary trimmers are the proper cutting tools. Scissors aren't precise enough and don't work well with the thickness of the pieces.
• A sharp blade is a MUST. The foam and thicknesses of the board will wear out knives more quickly than other materials. Most suitable tools have cheaply replaceable blades, make use of them. Otherwise the work will go harder and produce less clean results.
• Use a metal straightedge, preferrably with a lifting back (generally a strip of cork, raising the straightedge slightly) and vertical barrier (a short wall down the center of the straightedge), to ensure a clean, correct cut that doesn't damage your piece or yourself! Place the straightedge on the interior of the piece, such that only scrap material is damaged if the knife veers.
• Protect the surface of your table! Self-healing cutting boards can be found at any art or hobby store. Large pieces of fresh, scrap foamboard also works well for this!
• Do NOT try to cut through the entire sheet of foamboard with one slice. Many lighter cuts have less chance of skipping the knife, veering the cut, or damaging piece. They're also less tiring, an important consideration if making many pieces. Two or more cuts should be used to first break the top surface, clear away the foam, and finally break the bottom surface. Generally you can tell when the cut has gone all the way through by the change in resistance and sound as you move the blade.
• To make a piece fold nicely, e.g. for gameboards, simply don't cut through the bottom layer and completely through the sheet. This scores the piece and makes it fold easily without tearing or creasing. If the surface starts to wear over time, run matching colored or clear tape along the back. The cut will wind up the exterior of the fold, so for a gameboard you must cut on the back of the foamboard sheet to have the printed faces fold together. This doesn't look as exciting, but protects the printed surface better in travel.
• Make sure to angle the blade correctly! You want the blade perfectly perpendicular to the sheet. If the knife is held at any angle, you will wind up with a beveled edge. This is useful if joining pieces at a corner, but probably not desired for most game pieces such as tiles and chits. It may be worthwhile to acquire a knife with an integral guide to ensure 90 or 45 degree cuts, such as those at http://www.dickblick.com/itemgroups-f/foamboardcutters/.
• Lightly sanding the piece edges can remove any burrs created in cutting.

For an extended example, the walkthrough at http://rocketshipgames.com/games/centrerock/assembly.html uses foamboard to construct game chits and contains some more details and pictures.

As with most things, working with foamboard can require slightly more work than some approaches, but is frequently worth it for the aesthetic and durability benefits.