Pour your cream into your stand mixer (or blender)...no more than 1 quart at a time. Start mixing or blending on a low speed and as the cream thickens increase the speed.
After a while (5-10 minutes) it will go from being a thick cream consistency and will begin to look chunky.
Now look, it now has chunky yellow "beads" floating in liquid. This is your butter floating in buttermilk.
Now, pour off the buttermilk (save this..it tastes good and is good for cooking). Then, add some COLD water to your bowl and stir on low. Look how the mixing in the cold water has helped the butter clump together.
Now, it is any buttermilk that is left behind in the butter that will cause it to go bad in about a week. If you would like to save it and have it last longer you need to rinse it more. Just take a clump and knead it under cold running water.
I then took a cookie sheet and lined it with waxed paper. Then I measured the butter into 1/4 cup "balls".
I placed this cookie sheet into the freezer. I then placed the 1/4 cup butter balls into a freezer safe container so I can either use these for baking purposes or just defrost one ball at a time for other cooking use. (My 1/2 gallon of whipping cream made 3 1/4 cups of butter and 2 3/4 cups buttermilk).
UPDATE 2/19/2013: I found that using a food processor to churn your butter works very well. It is quick and since there is a lid, there is little mess.