The first part of cap and trade is the cap. The state puts cap on how much pollution is allowed. If an industrial plant or a utility generates more greenhouse gases then it is allotted, it has to go onto market to buy allowances to pollute.

The state is running this big auction, managing the sale of the rights to pollute the way the NY stock exchange manages the sale of equities.

"We also learned that we do not want to allocate all the allowances free, because we need industry basically to have some skin in the game," says Dave Clegern, with the California Air Resources Board, which designed and is running the cap and trade program.

More than 350 businesses including power companies, oil refineries and food processors are required to participate in the cap and trade program.

But the state wants to ease participants in, so for the first two years they only have to pay for 10 percent of their allowances, the rest they're given for free:

"The number of free allowances declines with a cap every year.  So while industry is getting 90 percent free the first two years, by 2020 they'll only be getting about 50 percent," Clegern says.

So as time goes on, participants are allowed to pollute less and have to pay for a bigger portion of their pollution.  By 2020, the state should be at 1990 levels of greenhouse gas emissions.

The cap on emissions goes down about 2 to 3 percent each year.

"As the cap comes down, there are proportionately fewer allowances available," says Clegern, which will likely drive the cost of allowances up.  "And it would become more beneficial, ultimately, to invest in reductions."

So some businesses will likely invest in greener or more efficient technology, for a variety of reasons. And some may reduce emissions below their cap.

That's where the trade -- or the auction -- comes in. These businesses will have extra allowances that they can sell to another business that hasn't been able to or chooses not to bring down emissions. The ARB has set a floor price of $10 per ton of carbon, so that the price won't become so inexpensive that it's more affordable to pollute.

And businesses that over-pollute can also buy offsets. The Air Resources Board is verifying certain projects that actually absorb greenhouse gas emissions, such as planting trees.

The idea is to give businesses some flexibility in when and how they reduce their emissions -- and use the market to manage those costs.

Long before the first auction this week, the market was already moving.

Samantha Unger Katz works for BGC Environmental Brokerage Services; her company has been trading carbon allowance futures over the past year in anticipation of the auction.

"Rules were adopted in June, we started to see the market price continue to go up. It reached a high of just over $20 a ton."

But then she says news came out questioning the legality of California's cap and trade program. Some say it's efforts to control the greenhouse gas emissions of power used in California could be construed as an attempt to regulate markets in other states. That would be unconstitutional.

"And since that point, we've seen a pretty steady decline in the pricing," says Katz.

Katz says rumors of potential litigation brought allowance prices to the lowest point since they started trading last year. She says the biggest risk for the market is the uncertainty of state regulations. Still, she says she's "cautiously optimistic."

It will take some time -- likely years -- to evaluate if the cap and trade program works. The system is designed to eventually regulate 85 percent of the greenhouse gases released in the state.

Even if it does succeed in reducing California's emissions, climate change is a global problem.

"What California is attempting to do is to become a model. And if you look at history, Calif has done this many times in the past," says Anthony Eggert, a former advisor to the California Air Resources Board.

California regulators have designed the program so that other states -- and even the county -- could implement it.

But long before that might happen, the nation is watching to see if California's attempt at cap and trade works.