Foam board gives decorators a lightweight alternative to plywood and other wood. In addition to being lightweight, it requires no special wall prep such as anchoring to hold even a large piece of foam board.
Double-sided tape is an option, but if you hang foam board on a painted surface, removing the tape might peel away some paint. Opt for tape that is removable and can be positioned without harming paint. You'll pay a little more than you would if you used your handy duct tape, but the end result for your paint is better. Place a piece of tape in each corner of the foam board and press it in place on the wall.
Hook-and-loop fastening systems, often referred to as Velcro, are a secure way to hang foam core. Buy dots or strips with removable adhesive to protect the hanging surface. Put a hook and loop together so they cling. Remove the paper backing from one side and stick it onto the foam board. For large items, place a dot or strip in each corner. Smaller items may need only one centered dot. After sticking the needed pieces on the back of the foam board, remove the paper backing from the sets and press it in place on the wall as desired.
Separating the hook-and-loop system by placing the hook on the wall then trying to match the loop onto the back of the foam board rarely works like you want it. Keep the pieces together to make application easier.
Cut a piece of thick string or yarn to stretch across the back of the project. Don't pull the string too tight; it needs to give a little. Hot glue the string to the back of the foam board. Stick a thumbtack, nail or picture hook into the wall and slip the string over it to hang. Slide the foam board around until it is balanced.
If you don't have a hot glue gun, duct tape can hold the string in place.
There are hangers made especially for foam board. Push the prongs into the back side or the top edge of the foam board and hang. Some foam hangers are made to slip tightly over the edge. Part of this style of hanger is visible.
Other hanging hardware can be used on foam board. Sawtooth and D-ring hangers are ways to hang wooden frames and large decor. They can work on foam board, too. Hot glue them in place on the back of the foam board.
Large items such as a foam board headboard should be hung with D-rings or hook -and-loop strips to hold the foam headboard securely in place.