The first step is to locate the studs using a stud finder. Typically, the studs in your wall are 16" on center leaving you with a 14 1/2" space. After you build the sides, you will have a width of around 13 - 13 1/2". Use a large level to draw a line on the wall where the studs are as well as the top and bottom. If there is an outlet or switch on that wall make sure you know whether the wires are coming from your basement or attic. If you have electrical running through the wall where you want to put your niche you will have to move it or patch the drywall back in.
There are several materials you can use for the backing -- 1/4" bead board, ship lap, mdf, 1/4" plywood, ect. I used beadboard. You cannot nail or screw the backing in or you will see the nails or screws on the other side of the wall. Use liquid nails. Cut your material to the width and height. Spread a generous amount of liquid nails onto the wall and press your backing in.