In order to craft clothes and weapons, you have to perform the following steps:
1. Gather some raw materials. This can be achieved from random work events or from expeditions you launch. You can check the amount of raw materials you own from the Warehouse window. In the beginning, what you need is plain (blue) materials.
2. Unlock the technology necessary to build the proper building (Tooling for the Armorer, Tracking for the Tailor).
3. Build the Armorer or Tailor shed.
4. Assign workers to the building, at least one worker should be assigned in order to craft objects.
5. From the building details window, select a recipe you have the materials to afford.
There you go! Your crafting process should be started.