A Bucket holds 10L of liquid.
To fill a Bucket with Water, click it to pick it up from the inventory and Right Click a shallow body of water while holding it with the mouse. (do not left click otherwise you will lose the bucket)
Once the Bucket is full of water a Lime stone can be added to it (Left Click on Lime, Right Click on full Bucket) to make Milk of Lime. Alternatively a Brain can be added to make Tanning Fluid. Alternatively, a Brain can be added to the Bucket to get Tanning Fluid, or Rose Otto can be added to a Bucket of Vegetable Oil to get Rose-Tinted Tanning Fluid.
A Bucket will also hold Blood drained from an animal heart.
You can empty a bucket by Right Clicking on it and choosing 'Empty', or by picking up the bucket and Right Clicking it on an empty Barrel (or a Barrel containing the same fluid that has room for the amount in the bucket).
An empty bucket can be filled from a Barrel by picking up the bucket and Right Clicking on the barrel.