Butter has been a part of the human pantry for about a week short of the time we have been keeping cows. When cow's milk (straight out of the udder, homogenization and pasteurization are still centuries in the future) is left still, the cream floats to the top. Cream consists principally of the components of whole milk that have a lower specific gravity--mostly, the fat. Milkfat in its natural state is contained in "fat globules," which, exactly as they sound, are microscopic lumps of fat suspended in a liquid composed mostly of water, with a little protein mixed in.
The upshot of all this dry chemistry is that if you take cream and agitate (or "whip") it for a little while, you can break up some of these globules and introduce air into the mixture. If you whip it more, you'll break up more and make the cream stiffer. If you whip it even more, you'll reach the point where the globules collect into masses so heavy that they displace the air, collecting into a solid mass. This solid mass is what we call "butter."
The word "butter" derives from the Greek "boutyron," in turn derived from "bous" (meaning "cow" or "ox") and "tyros" (meaning "cheese"). Of course, many kinds of cheeses are made from cow's milk, but most cheese in ancient Greek times were made from the milk of sheep, and while butter is a high-fat solid dairy product, that is as close as a resemblance to cheese as it gets. Nonetheless, we needn't count the ancient Greeks at fault for having nomenclature that differs from ours.
What should we do? Why, we should make butter! Read on for further details.
Step 1: Start With Cream
The only physical ingredient involved in the making of butter is cream. Indeed, the process of butter-making doesn't involve adding things to cream as much as it does taking them out--to wit, buttermilk. We got our cream at Costco. and I think the price was something on the order of $6 for a half-gallon. Figure on getting about half the cream back as butter.
Also: try to buy a cream that is as unadulterated as possible. Some commercial creams contain carrageenan (a natural thickener derived from a type of seaweed native to the Irish coast) or other thickening agents, and while I don't think it'd be impossible to make butter in the presence of such, the end product wouldn't be as good. You don't need to go down to Farmer X's stand and buy the cream he got from yesterday's milking (although butter made from such cream would probably be excellent); you just need to get something that has in it more natural product than plastic.
Step 2: Churn the Cream
Now it's time for a step that was traditionally related with backbreaking physical labor--churning the butter. Fortunately, you live in the era of electricity, and more importantly, the electric motor. So take your electric mixer and go to town on your bowl of cream.
Naturally, the first step in your process will be whipped cream. Have patience, As the fat globules continue to break apart, you'll get stiffer whipped cream, and even stiffer, until suddenly, the little lumps of butter start to slosh around in the buttermilk. Again, this happens quite suddenly, but you'll know it when you see it, even if you haven't done this before--it's a quick, qualitative change, not like that between whipped cream and slightly stiffer whipped cream. You'll go from having very stiff and slightly sloshy whipped cream to having very broken-up butter and very sloshy buttermilk in a matter of seconds.
Also: recall that whipped cream has a significantly greater volume than that of plain cream. Whip your cream in a vessel that has enough spare volume to allow for this expansion.
Step 3: Wash the Butter
Now it's time for a step that isn't often mentioned in chronicles of butter-making--washing the butter. There are still milk solids left behind in the butter that didn't make it into the buttermilk, and so it's vitally important to wash the butter if you want to keep it for more than a day, even in the refrigerator. To do so, knead the butter until all the liquid comes out, and then run it under a faucet while kneading it, and continue until all the liquid runs clear.
Step 4: Enjoy!
Now you can use the butter! While I most frequently enjoy butter on toast, you can use it in any way you enjoy it--sauteeing onions, making ghee, on mashed potatoes, or whatever. Butter is most versatile, and as you went to the trouble of making your own, you deserve to enjoy it any way you like.