Begin by culturing your cream (this is an overnight process, so plan accordingly). In a clean glass or ceramic container (bowl, jar, etc) combine the cream and yogurt, crème fraîche or buttermilk. Cover loosely and place it in a warmish part of the house - the ideal temperature is around 75F (23C), but anywhere in the range from 70-80F (20-26C) is okay.
After 12-18 hours, the cream should be noticeably thicker and should taste slightly tangy, i.e. like crème fraîche. If it's bubbling and gassy, some unwanted bacteria have gotten in there so discard your cream and start again (note that this has never happened to me). If it hasn't thickened yet, leave it alone for another few hours and eventually it will. When your cream has thickened, if you are not ready to make your butter right away, transfer the container to the fridge where you can leave it for up to another 24 hours.
In order to churn properly, the cream needs to be at about 60F (15C). If you're taking it out of the fridge just let it warm up until it reaches this temperature; if you're making it from room temperature you'll need to place the bowl in a bath of ice water for a few minutes to cool it down. Also, fill a large bowl with water and ice cubes and keep it handy.
You can use any method you want to beat the cream; handheld electric beater, stand mixer, etc - even whisking by hand. Basically, just put the thickened cream in a clean, deep bowl and start beating as if you're making whipped cream. When the cream starts to form stiff peaks, reduce the speed to low. At this point watch carefully; first the peaks will start to look grainy, and a few seconds later the cream will break. When it does you'll know it - globules of yellow butterfat will be swimming in a sea of buttermilk, and if you're beating too fast you'll have buttermilk everywhere. Stop beating and carefully tilt the bowl over a cup, holding back the butter clumps as best you can, and drain away as much buttermilk as possible. You can use this just like commercial buttermilk, by the way, and it's delicious.
Now you have to wash the butter to get rid of all the residual buttermilk, which would cause it to spoil prematurely. Using a fork (my preferred implement) or a stiff rubber spatula, pour some of your reserved icewater over the butter, kneading and stirring it around vigorously. The water will turn whitish and the butter will firm up, making it cohere and knead more easily. Pour out the liquid and repeat as many times as needed until the water sloshing around in your bowl is completely clear. After you've poured off the last of the liquid, continue kneading for a few more minutes to get as much water as possible out of the butter. If you want salted butter, add your favorite salt now, to taste.
You've now got a generous supply of your very own cultured butter. Pack it into ramekins, roll it in waxed paper, or fill cute little molds with it before refrigerating; I recommend freezing some if you won't be able to finish what you've made within a week or so. Whether storing it in the fridge or freezer, though, keep it tightly covered, as butter is a sponge for other aromas.