There are many different sidings you can use, from pine tongue and groove to cedar or others, all depending on your budget. Plywood is even a great option.
You can run your boards vertically or horizontally when installing your siding, but keep in mind, vertical installations use more lumber. Cut your tongue and groove boards to size, measuring and cutting as you place the boards.
Start at one side of the frame and secure the boards using 1 ¼-inch brad nails. Insert the groove to the previously placed exposed tongue and continue placing boards like this, securing with brad nails at an angle at the top and bottom of the frame.
You may reach the corner with a short or long board. A gap of approximately ½-inch will be ok, otherwise you may need to measure and mark a new board and rip it down lengthwise with your circular saw to complete one side. Continue placing the boards like this around the house until completed.