The Measure tool is found on the left hand navigation menu. Currently, it is the last icon in the list on the left, and looks a bit like a ruler over the top of a pencil. (Example to the right)
The measure tool is a great addition to the tools in Google Earth. Now, just like in the desktop version of Google Earth, users can use the measure tool to create lines, perimeters, and shapes. When you create a line, the measure tool will display the distance of the line. When you create a shape, the measure tool will give both the distance or perimeter and the area of the shape.
In the settings menu of Google Earth, found by clicking on the menu in the upper right corner, and then selecting Settings from the drop down menu, you can configure your units of measure.