It's all about the difference in size between two gears. Using the smallest gear on the front with the biggest gear on the back gives you a lot of power but not much speed. That's good for going up hills. Using the biggest gear on the front with the smallest gear on the back gives you a lot of speed but not much power. That's good for going down hills. Your left shifter lets you move the chain from one front gear to another. The right shifter lets you move the chain from one back gear to another. To start, put the chain on the small gear up front and one of the middle gears on the back. As the terrain changes, shift back gears so that you only need light but steady pressure on the pedals and can move them rapidly. If you run out of back gears, shift a front gear. There is more to it than that, but this should get you started.
HTH