Just lived this Saturday night at the St. Mary's County Fair. Went in with a buddy (he bought) simply to learn how it works.
There were far more pigs to cows. Like 75 vs. 20. They split them up into groups and every animal goes on a list with a number along with their specs (owner/raiser, weight, etc.). If you plan to participate in the auction, you need to register. This will give you a number to bid with. I believe it was free to register.
They start auctioning off the prize winning animals of the class. They typically fetch the highest price per pound (this is the unit they auction with) and these animals often go to companies who are specifically supporting that particular 4H member or are simply looking to essentially donate the money. IE - the meat from the prize winner tastes no different than another cow later in the series. So, wait this out.
If you want to bid with someone (splitting a cow), it's usually best to either have this arranged ahead of time by asking around (websites, various 4H groups, etc.) or simply asking around prior to the auction. When you bid together (and each are handling your own cost), you have one person bid who holds up both cards.
Anyhow, the auction is just like any other. You stay in until you want out. Well run IMO. Pricing for beef went for anywhere between $2.10 - $2.50/lb. Most were in the $2.30/lb range (which is what we ended up with). Weights were in the 1000 - 1300 lb range. Also got a pig for $1.25/lb I believe. Weights were 200-310 lbs for the hogs.
This is what you pay on the live weight and goes back to the 4H person for their purchase of their cow. From there, there was a list of three selected butchers (Chucks out of Charles County/Bryan's Road, another in Prince Frederick and a 3rd on the eastern shore .... began with an "S" and has been part of this for years. Just can't remember it off hand). The eastern shore place was the cheapest (but of course, the farthest). For cows, prices were between $0.55-$0.75/lb for processing plus another $35 for a kill fee (Hetzlers). The eastern shore location was right at $0.50/lb and had no kill fee. There may have been a modest delivery fee with all three.
When you "win" your animal, you go to the fair office to pay (check) and pick your butcher. They will apparently call you later in the week to select your cuts. Their charge is based on the hung weight (think field dressed like with deer). This is basically skinned, low limbs/head removed, etc. What you'd see hanging at a butcher or being punched by Rocky.
There are all kinds of "math" formulas out there to determine net meat yield vs live weight but I'm clueless. All in all, the number my buddy mentioned left the unit price (per lb) high for ground beef and low for cuts (steaks, etc.). He's done it many years so he has to believe there is a value there. He usually splits a cow with someone, but even with my family of 5, we just don't eat that much beef in a year.