The rule of thirds is very simple. You divide the frame into 9 equal rectangles, 3 across and 3 down as illustrated below. Many camera manufacturers have actually included the capability to display this grid in live view mode. Check your camera’s manual to see how to turn on this feature.
In this photo, the horizon roughly along the bottom third of the frame and the biggest and closest trees along the line to the right. The photo wouldn’t have the same impact if the larger trees had been placed in the centre of the frame.
You should place the most important element(s) in your shot on one of the lines or where the lines meet. It works very well for landscapes as you can position the horizon on one of the horizontal lines that sit in the lower and upper part of the photograph while the vertical subjects like trees or mountains can be placed on one of the two vertical lines.