Historically, rustic furniture was made from whatever natural materials were in the greatest supply, often by poor people as items of trade for food or cash.
More often than not, the basic material of rustic furniture was willow, although many other types of hard and softwood were also used.
Below are several site where you can find plans and instructions for building various types of rustic twig furniture.
Find free plans to create a beautiful, rustic bench that costs almost nothing to make. With a a full materials list, tool list and step-by-step instructions. http://www.homeenvy.com/db/9/79.html
Here you'll find simple instructions and step-by-step photographs for making a small willow table. http://rockycanyonrustics.blogspot.com/2008/03/simple-twig-table.html
Illustrations and instructions on making a willow chair can be found here. http://www.freecraftunlimited.com/willow-chairs.html
Here are links to instructions for a more complicated hanging swing. It includes: Preparing the Timber/Cutting and Assembling Back Spindles and Frame/Joining the Sides/Weaving the Seat/Finishing and Hanging the Swing. http://www.diynetwork.com/DIY/shows_diw/episode/0,2046,DIY_14299_25729,00.html