The Stern Report described climate change as "the greatest case of market failure" the world has seen. In fact the market has not failed – there is no market at all. There is no market in war, either, which some think more devastating then climate change. Markets deal with transactions, not with human behaviour in general. Where there are no exchanges, there are no markets.
Markets can prompt and regulate human activity by signals they send about scarcity and prices. They allocate scarce resources in ways that encourage people to consume less of them and produce more of them. When some resources, such as air, water, and ocean fish stocks have no price on them, there are few restraints on their use. Sometimes production causes 'externalities,' such things as pollution and noise disturbance, and the depletion of resources.
The way to have markets protect the environment is to put markets into place. If some activities contribute to climate change, there should be a price to pay for doing them. The habit of environmental campaigners of picking out relatively trivial symbolic targets such as "food miles" or budget air travel obscures the fact that agriculture, industry, and power production are among the greatest emitters of "greenhouse gases."
Markets can be introduced by putting a price on previously unowned resources. Fish quotas can be set and then traded, giving the buyer ownership of the fish and an incentive to conserve them. Tradable emission permits can discourage emission by raising the price of doing it. They raise production costs to those who emit more, and reward efficient, cleaner producers.
Markets can be used to promote the development of clean technologies by giving them a price advantage, encouraging people to produce more cleanly by making it more attractive financially to do so. Markets can protect the environment if they're properly introduced.