Simple:
1x2 stock, nylon screen material. Build a square/rectangle of 1x2 material the widest part places your "depth" of the tray. Lay the screen over that, stretch and staple around the sides.
When you use them the screen is up. Your first tray should sit on "legs" which can be as simple as four bricks which allow airflow from beneath.
For sun drying, place an empty tray over that (to keep the bugs off) in the full sun.
For air drying, you can stack trays as many as you may need.
When you cut what ever you are drying, cut it thin and lay it out with 1/2 to a full inch of space between each slice. Drying depends on humidity.
http://www.seasonalchef.com/preserves21.htm gives "recipes" for some of hem, dips and preteating preserve color of many things.
http://teriskitchen.com/preserving.html has some helpful information as well.
You can even dry food in the oven, if you have a pilot light that is all you need, if you have electric over you need to set the oven on warm (lowest temp).
You can dry anything without further treatment, however things will tend to look strange, discolored. Most fruits turn into "leather" or rubber.
The only real con I can think of is all the preparation, thin slicing and the long drying time.
David