The Sink comes with two functions: by itself, it can be right-clicked to fill buckets with water, clean dyed wool or armor, or just make fun water splashes. When it is used as part of a multiblock kitchen, recipes that require water buckets (or Pam's Fresh Water) will automatically use water from the sink (some may still require a bucket though).
Check the Cooking Table for more information on Multiblock Kitchens.
Right-click with a bucket to fill the bucket with water. Right-click with dyed wool or armor to clean the color off.
Some modpacks may require you to pump water into the sink for it to be functional.
The Sink, like many kitchen blocks, can be dyed by right-clicking it with a dye.