Cut a circle out of 1-inch plywood the desired diameter of the well with a saber saw. Wrap a length of stiff wire with 2-inch holes around the circle. Cut the wire fencing with wire cutters and wire the ends together. Wrap another layer of the wire around the first layer with the holes offset. Cut and fasten the ends together with wire. The plywood is now at the bottom of a wire column. Trim the column down to the desired height. Position the framework in the spot where the well will be located.
Place two 2-inch by 4-inch boards about 8 feet long inside the well. Use a carpenter’s level to adjust the boards so they are straight. Wire the boards to the frame from the bottom up to the top of the wire column. Make sure that the boards are directly opposite of each other. Nail a 1- or 2-inch diameter dowel 12 inches from the top of the boards. This piece stretches between the two boards and keeps the boards from flopping over near the top. Straighten any bent areas in the wire column. Try to keep it as perfect a circle as possible.
Pour dry cement mix into a large wheelbarrow and break up any clumps with your hands. Mix in the amount of water indicated by the directions on the package. Spread a layer of cement ½ inch thick 12 inches up the side of the column using a cement trowel. As you work your way up the column, add more wet cement.
Cover the back, top and bottom of the stones with a thin layer of cement. Place the stones in rows around the column by pushing the stones into the cement layer covering the wire. Do not push so hard that the wire bends. Keep working around the well in rows until your reach the top of the column.
Spread more cement across the top of the stones and wire column. Add the last layer of stones in a level layer to create a rim around the well. Let the cement dry for 2 hours. Squeeze grout designed for outdoor use between each stone. Wipe any excess grout off the face of the stones with a wet rag.
Cut two triangles from 1-inch plywood that measures 36 inches on each side. Measure the across the top of the two boards that will hold up the roof. Cut two rectangles of plywood measuring 36 inches on one side and the distance across the top boards plus 2 inches.
Screw the two rectangle pieces to the triangles with an electric screwdriver to form the roof. Fasten the roof to the upright boards with screws.
Paint the wooden pieces of the well with outdoor paint. Let the cement dry for 2 weeks.