People that still make their Plum brandy usually grow about 20+ trees in their garden. A very skilled Slivovice maker will pick only ripe and healthy plums of the tree in the fall. He will not use the ones that had fallen down on the ground few days before, because they are too ripe. A Slivovice master will put plums into big barrels and will let the plums ferment for several months in the shady, yet fairly warm area (usually barn). A foamy plug will develop and it will shield the liquid under neath from environment, and millions of live active coultures will help the plums to develop into a mixture that later on will be turned into Plum brandy with special "cooking" machines. Nowadays, there are companies that will store your barrels and then "vypali" (cook) your brandy.
When consuming Slivovice, you should smell it (like wine), then drink it and swallow it fast. It is said that the best Slivovice is velvety, smells after plums, you do not feel any burning of alcohol and after you drink it, there should come warmth from belly all the way to your throat without any funny taste residues.
I found a video (see below), that will show you the tradition of Slivovice making. The song accompanying the video is about the Slivovice making and the life with it. If you ever visit Czech or Slovak Republics, beware of drinking too much of it. Two,three or four shots should do it :-) Do not try to keep up with locals!!! (The perfect Slivovice will have 50% of alcohol in it!!!)
Also Slivovice is considered a medicine for belly ache (just like Becherovka) and headaches. So if you get a headache by drinking too much Slivovice, you better fix it with Slivovice :-)
Credit: The above image is a property of Zelenina Kovar (Czech farmer)