If you have a premium Second Life account you can own land. But to own land you will have to buy it.
There are several ways to acquire a piece of land in Second Life. Here are the most important ones.
When new land is available in the Second Life World, it could be posted in an auction system. The mechanic of the auction system is similar to common platforms like eBay. The bit can be made in Linden Dollars or US Dollars.
If the resident has not owned a piece of land yet, he gets land via the "Land for Landless Program". About 500 square meters will cost about 512 Linden Dollars. It will take some days before the land is fully available for the buyer - but it is guaranteed.
In Second Life finding the right land is possible with the "Find" window. In the category "Land", size and price can be specified. Also if the resident wants to buy the land straight away or wants participate in an auction. After making the choice the resident has to maneuver to the land. With a right click on the land the "About Land" menu opens. Is the land for sale, the resident can acquire it.
Menue "About Land"
There is another way to research for land. The resident can change the map view using the dropdown menu. Land for sale will be displayed in white. Land that is available through an auction is displayed in purple.
Of cause, for bigger projects there is always the possibility to buy a whole island.