They buy it at market value. Someone donates it for zero money. They buy it at a bargain price. They use grants to purchase it. They hold conservation easements, or they only manage it.
Some land trusts are very particular about the lands that they receive or purchase.
The Nature Conservancy, for example, only takes land that has endangered plant or animal species on it, or that in its entirety is itself an endangered habitat or ecosystem. Other land trusts, such as the Trust for Public Lands, spend their time being intermediaries between smaller land trusts and government agencies that may not currently have appropriations to purchase high priority land, and the land owner that needs to sell as soon as possible. These trusts purchase the land to hold it until those agencies can find the money. In this way, land trusts have assisted state and federal governments as well as small local land trusts tremendously. At that time, a generous man named Albert Sewell donated 35 acres outright.