Take Measurements and Order the Window
You'll need to order your garden window several weeks in advance. Garden windows come in a variety of sizes and shapes, but all provide similar elements: extra shelf space and at least four sides of glass, including the top sloped glass.
Order the new window based on the rough opening size of the window you are replacing, not upon the unit size. That means you'll have to remove the old window and be prepared to cover the opening with a temporary cover (e.g. plywood) until the garden window arrives.
After removing the old window, any trim pieces, nails or old flashing, measure the rough opening very carefully. It's also a good idea to check to see if the rough opening is level, plumb and square.