At sundown today, the Dipolieia festival starts, and in ancient Hellas, the Bouphónia was held on this day. I have written about the Bouphonia before; the post can be found here. In short, the odd ritual of the Bouphónia comes down to this:

"Every year on the fourteenth day of Skirophorion, from the time of Erechtheus (1397 - 1347 BC) to--at least--the second century AD, an odd ritual was reenacted. It was called the 'Bouphónia'  (βουφόνια), and was part of another festival; the 'Dipolieia' (τὰ Διπολίεια), a feast in honor of Zeus Polieus (Zeus of the City).
 
On top of the Acropolis, the oxen are released from the temple of Zeus Polieus. Outside lie cakes on a table, and the oxen are herded past them. Nearby, two women with bowls of water in their hands and a man who is sharpening an axe and knife watch. One of the oxen in line reaches for one of the cakes and devours it. One of the nearby men shouts at the ox, and rushes to the man who is sharpening his weapons. He grabs the double-bladed axe and with one big swing, ends the life of the ox. The Ox-Slayer drops the axe and flees the scene. The slain animal is sacrificed properly to Zeus Polieus. And a hunt begins for the murderer of Zeus' sacred ox. He is found and brought to trial. The blame is passed from the Ox-Slayer, to the man with the weapons, to the women with the water and eventually the weapons themselves. They are found guilt and tossed off of a cliff. The ox is stuffed and put out on the field, in front of a plough.
 
[...] It seems to me that there is an underlying theme to this myth, and its subsequent festival: that an animal which is slaughtered by a man alone, is killed, yet an animal which is slaughtered by a group becomes a sacrifice. Everyone is 'to blame' for the death of the ox, simply by being there, and in order to break the circle, an inanimate object--which, obviously, cannot defend itself, thus the cycle cannot possibly continue--is chosen to bear the blame, thus taking it off of everyone else. "

The Bouphónia is an ancient ritual, archaic even in classical times. It's most likely best to simply celebrate the Dipolieia, and not the Bouphónia. A simple libation to Zeus Polieus will do. If you feel the need, you could always perform a version of the Bouphónia where no animals are killed, but a (clay or wax) figurine is slain, sacrificed, and the blade that killed it (also clay or wax) is destroyed.