A Sketchbook in ALOFT allows you to sketch various pieces of buildings that you find on islands, thus unlocking their building formulas. To craft a Sketchbook, mix on a workbench: 2 Wood, 1 Paper, and 1 Charcoal.
After crafting, place the Sketchbook onto the quick access panel and take it in your hand. Hold the Right Mouse Button and aim at an object you would like to sketch (for example, a table or a chest).
If the object can be sketched, you will see the materials required: 1 Charcoal and 1 Paper. Press the Left Mouse Button to sketch the object and unlock its formula.
Do not sketch thoughtlessly, as paper in ALOFT is quite a rare material, especially in the very beginning. You can obtain it by collecting books, which can be found on various islands.