Put the butter into a good-sized nonstick pan. Melt at the lowest possible heat.
When it's all melted, increase heat slightly. There must be no sign of smoke or any other undue activity indicating too much heat. Leave the butter to stew (the only word for it, really) for about an hour. Watch it carefully to make sure it doesn't get too hot and start to scorch. The milk solids will fall to the bottom of the pan: others will float on top.
Don't Stir or agitate the pan under any circumstances!
At the one-hour point, carefully skim off any remaining floating stuff with a skimmer or slotted spoon. Remove the ghee from the heat and allow it to cool for 10-15 minutes. Strain it into a heatproof jar through a triple thickness of cheesecloth, or a thickness of butter muslin if you can get it, or even through paper towels.
The ghee will solidify, but it won't get too hard. It should be light yellow and have a lovely butterscotchy aroma. Keep it tightly covered in a cool place. It will keep almost indefinitely if you've successfully gotten all the milk solids out.
Cholesterol alert, for those needing one: This is 100% pure butterfat. Use in moderation.