This is a overnight process, so plan accordingly
The first step is to culture the cream overnight. Modern cream is ultra-pasteurized and lacks the active dairy-friendly bacteria needed to bring out a full flavor. To rectify this, culture it with some yogurt to bring out a full flavor for a European-style cultured butter. You can make butter without this step, but it'll wind up just like store-bought American butters and isn't really worth the effort.
1. Transfer the cream to an inert bowl (glass is ideal); make it big enough that you'll be able to whip it without overflowing.
2. Add the fresh yogurt, stirring it gently to mix in the yogurt
3. Cover loosely, and let it sit in a warm-ish (70-75 degrees F is ideal) location for 12-18 hours.
After 12-18 hours check on the cream. If it is bubbling and gassy then you should discard and start again (so I hear; I've never witnessed this). It should have thickened somewhat (not a ton, but enough to notice if you dip a spoon in it). If not, let it sit another couple of hours.
The final step in preparation is chilling slightly to about 60 degrees F. Either refrigerate for 45 minutes or so, or use an ice water bath to quickly chill it a bit.
Now you're ready to churn. Grab a hand mixer and start whipping on high as though you're making whipped cream. Once you have whipped cream, keep going. You'll notice it starting to clump or yellow; at this point turn the mixer down to low but continue whipping. At some point the cream will "break"--all of a sudden the butter and milk will separate, leaving a liquid in the bowl. Stop beating immediately.
Reach in and lift out the butter, squeezing it together into a ball (and expelling more buttermilk). Drain off the buttermilk into another bowl and use it as you would any buttermilk. Now you need to rinse the butter. Add a small amount of ice water, work it through the butter, and discard. Repeat until the water added is clear. At this point, the butter is done. Work some salt in if you want it salted (or get creative with chives, garlic, red pepper, or anything you like). shape it in molds or press into small bowls. Cover it and refrigerate (or freeze for longer-term use).