White Russian are made with vodka, coffee flavored liqueur, and cream. In most cases, people use Kahlúa as the coffee liqueur, although other brands such as Tia Maria will work as well.
Despite its name, this drink didn't actually originate in Russia. Instead, the Russian reference comes from the fact that it contains vodka as one of its primary ingredients.
The basic idea for the drink actually originated in Belgium in 1949. A bartender named Gustave Tops developed a drink called a Black Russian in honor of the U.S. ambassador to Luxembourg, Perle Mesta that combined vodka and coffee liqueur over ice in an old-fashioned glass.  The White Russian came along some time after when people started adding cream to their Black Russians. Although there is no exact date available for when the first White Russian came into being, it is generally believed to be sometime in the 1960s. 
Although recipes for White Russians vary, they typically mix 2 parts vodka with 1 part coffee liqueur and 1 part heavy cream. Start by filling a rocks glass or old-fashioned glass with ice. Pour the vodka and liqueur over the ice. Top it all off with a layer of cream.
If you want the cream and alcohol to stay layered to create a two-toned effect in the glass without mixing, Kahlúa recommends pouring the cream in slowly over the back of a spoon. 
Here's a great video that shows the process step by step: