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
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
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.