Here I am going to show two different ways to mount artwork on a flat board.
The first will be a simple way that you, the purchaser can mount the art yourself on foamboard.
The second method is the way that I mount paintings that have to be shipped. With this method, I mount the artwork on tempered masonite board, rather than foamboard, because it is tougher and less likely to be damaged in transit.

 Go to a building supply store like Home Depot or Lowes and buy a sheet of 1/2" insulation sheathing. It costs about $10.00 for a 4' x 8' sheet.  While you are at the store, buy a bottle of carpenters' glue and some wall anchors.

The insulation board is easy to cut with a razor knife or box cutter. Measure the artwork and add 6" to the width and 7" to the height, for a border.

Here is the board, cut to size and ready to paint. Choose a color that compliments that in the painting.

After the paint has dried, position the painting on the board. Then put masking tape along one long side to act as a hinge.

Flip the artwork over to expose the backside.

Apply a strip of rubber cement around all four edges. make the strip about 1 1/2" wide. Do not apply the cement to the entire back surface.

Flip the painting back over. Smooth it out against the board and remove the tape. Allow to dry overnight.

You will need a hanging strip on the back of the board. Find a piece of wood 1/2" thick and about 2"-3" wide. Cut a bevel along one corner to catch your wall hanging device.

Apply wood glue on the "bevel" side of the hanging strip and apply it to the back of the board as shown. Allow to dry overnight.
Your artwork is ready to hang.

Here are three types of drywall hanging devices: A metal expansion hanger, a plastic screw-in hanger and a "monkey hook". The first two require a philips screwdriver. The monkey hook does not require any tools.

Whenever a purchaser chooses to have me mount the artwork, I always mount it on tempered masonite and reinforce the backside (as shown). The masonite is better able to withstand the rough treatment of shipping.