Place the butter in a medium-sized heavy-bottom saucepan, and set the heat to medium. Bring the butter to a gentle simmer. Once the butter is simmering, you'll notice a white foam begin to form on top. This means the milk solids are starting to separate and rise to the surface.
After several minutes, you'll begin to see and hear a change, which is how you'll know the clarified butter is almost ready. The simmering bubbles will become larger and make little popping sounds (watch out for hot, splattering butter).
When the bubbling slows down to almost nothing and the butter is transparent (you should be able to see the bottom of the pan if you move aside the solids with a ladle), that's when it's time to start skimming the surface. You can remove the pan from the heat first, or leave it on if the milk solids aren't browning. Try to get most of it, but it's ok if you miss some since it will be strained.
Finally, strain the butter through a fine mesh strainer lined with 1 or 2 layers of cheesecloth. This will catch any lingering solids.
Use immediately, or allow to cool and then transfer to an airtight container. Clarified butter will keep for up to 6 months in the refrigerator.
Notes
I recommend using a good quality European butter like Plugra or Kerrygold. It's not essential, but you'll be able to taste the difference.If you want to make ghee, follow the exact same steps, but simmer the butter until some of the milk solids sink to the bottom and brown. The browner the better, but make sure they don't turn black. Yields approximately 1 1/2 cups total.