Determining when plate tectonics began to function is very hard to figure out. Fortunately, some geologists think they may have solved this problem. In a recent paper published in Science, led by Ming Tang from the University of Maryland, researchers suggest that plate tectonics began 3 billion years ago. Geologists assume that granite appearing on the surface of the Earth is an indicator of when plate tectonics began. Before this, the surface of the Earth was composed of basalt, or other mafic rocks.
To make a long story short, mafic rocks, like basalt, have a lot of magnesium in them; whereas granite doesn't. If you can date the oldest rocks with low magnesium content (i.e. granite), you can determine the start of plate tectonics. Unfortunately magnesium weathers out of mafic rocks on the surface relatively quick and can't be used.
The research team used other elements associated with magnesium in mafic rocks which do stick around for a long time, such as nickel, cobalt, chromium, and zinc. By looking at the decline of these elements in mafic rocks, the research team was able to determine when plate tectonics began to function, about 3 billion years ago.