Here are some tips on gear shifting  on a bicycle:

• To ride smoothly on and more comfortably off-road, use slightly larger gears. This will enable you to support more of your weight on your pedals and get some off your bike seat, which allows “floating” over rather than pounding into roots, ruts, and other rough objects.
• Gear shifting on a bicycle works best when you apply only light pedal pressure.
• When riding uphill, shift before the climb gets too steep and do not stomp on your pedals until the shift has taken place.
• Change gear whenever you feel that your pedaling gets either too hard or too easy.
• When you feel that it’s time to shift, use your right shift lever for small adjustments in your pedal effort and use your left level for major changes in how easy or hard it is to pedal.
• Anticipate shifts. It’s both bad for your bicycle and difficult for you to shift gears when you’re pushing your pedals very hard. So make it a habit to downshift into an easier gear as you begin to approach a big hill or come to a stop. Do not try to change gears when you’re stopped. Bicycles with traditional gearing are designed to be shifted when pedals are moving. However there are modern multi-geared bicycles which allow gear shifting anytime during a ride, whether or not the pedals are moving.
• Avoid cross-chaining. It is hard on your sprockets and your chain to be at extreme angles. So to avoid this, remember, no shifting gears on a bicycle to a spot where it is on the smallest ring in the front and smallest gear in the back, or vice versa, on the big ring in both rear and front. The put your chain on opposite extreme ends of the spectrum. And if you find yourself in this type of situation, that is a good sign that it is time for a big front gear shift. This helps bring things back in sync.