There is a left and a right side of the handle bar twist shifters on that bike. The left side controls the front derailleur, the right controls the rear. Twisting that part of the grip changes the gear. It moves the derailleur by cables. The derailleur is the mechanism that moves the chain from gear to gear. Only shift when you are pedaling. If you are not pedaling it won't shift.
When you shift: The big gear on the back is easier to pedal, the small gear on the front is easier to pedal. The small gear on the back is harder to pedal, and the big gear on the front is harder too. Only shift when you are pedaling.
The idea is a lower gear (larger back, smaller front) is for when you need power. Like to start out or up hills. You will pedal faster and not go as fast. You should shift into the higher gear (smaller back and larger front) when you are going down hill or cruising.
Get out and ride. A little practice and you will have the hang of it. Shifting and riding becomes second nature after a bit.