Bon Soir, Benoit. I would really think twice about building wood storm windows. Aluminum or vinyl storms are relatively inexpensive and work well. Wood has to be painted often, annually in some climates.
It can be done pretty easily with the right tools. This would include a good quality contractors saw and a router/router table or shaper. My guess is that if you already own these, you might have the knowledge to build any door. There is not much difference between how you would build a door for your kitchen cabinet and how you would build a wooden storm window except the shapes that you mill on the edges of the wood. About any rail and stile bit set and an extra rip cut will make the wood part.
You will want to use acrylic or polycarbonate glazing, probably. There are building code requirements for glazing and this includes storm windows since breaking and broken glass is the issue. The "plastic" is better, safer and easier to use than glass. Such things as "Historic District" requirements may also be an issue for you, though. Have a professional glass shop cut some of the glazing for you and show you how to install it on a window or 2. Some shops will work with you for a few extra bucks for their time.
If you don't have the tools I mentioned, you would be looking at $600+ US just for this. You would not want to skimp to much less than that. Wood, glazing and extras like paint, glue and clamps and glazers points will add to this. More details of what you really want to do might change some parts of this slightly, but the basic info is correct.