Right-clicking on a placed Part Builder will open its GUI. On the right side of the GUI is a short how-to description:
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Here you can craft tool parts to fulfill your tinkering fantasies. To craft a part simply put its pattern into the left slot. The two remaining slots hold the material you want to craft your part out of.
— Part Builder
The GUI has three slots on the left (for input), an arrow denoting input to output sides, and two slots on the right (for output).
The far left slot has a square icon and is for patterns. If there is a Pattern Chest next to the Part Builder, the contents of the chest can be accessed from within the Part Builder GUI.
The ingot and cube slots are for raw materials (e.g., wooden planks or Obsidian blocks). The pattern tooltip will display how much material the part requires. If there are materials in the material slot, the material value will be displayed below. The right side of the tooltip will display useful information about the material, such as its durability, mining level, handle modifier value, and properties.
When enough of the material is present in the Part Builder for the part, the output slot will be filled. Like a vanilla Crafting Table, the materials will not be consumed until the finished part is removed from its slot.
The far-right slot with a shard icon is for leftover materials. In previous versions, patterns in Tinkers' Construct used smaller material amounts such as 0.5. In versions after 1.7.10, only the shard pattern produces a fraction of a material, so the shard mechanism is virtually deprecated.