Supports Not Required
No supports are required for either part, whether you are using a single or dual extruder. The overhangs on the edges are all no more than 0.5mm, which is small enough that most printers should have no trouble. The grooves for the lid have a 45 degree overhang, which should print fine.

You will need good bed adhesion, otherwise the parts will not fit together properly. A heated print bed is recommended. If you do not have one, use your favourite method for ensuring that your print sticks to the bed (a wide brim may help), and monitor the print for the first several layers.

Single Extruder
Print crafting_table_box-single.stl and crafting_table_box-lid.stl. The infill setting doesn't matter much, although you should use at least a bit of infill (20% works well) to give the walls some strength.

Dual Extruder
Combine the crafting_table_box-wood.stl and crafting_table_box-metal.stl files for a two-tone print. The lid (crafting_table_box-lid.stl) is only one material. Print the "metal" part solid (100% infill). The "wood" part should have some infill (20%) to give the walls some strength.

In a two-material print, the "metal" parts of the design are a collection of small pieces. Many printers have a hard time printing shapes this small. For best results, slow both the print and travel speeds and accelerations way down. Not much of the "metal" material is used, so this won't have a huge impact on your total print time, but it will improve your results.

The pictures shown here were printed with FibreForce Wood Infused PLA and Ultimaker Silver Metallic PLA on an Ultimaker 3.