1. As a general rule, leave your front shifter in the middle chainring position and forget about it. Now you can concentrate most of your shifting on just your rear shifter.
2. If you find yourself panting or out of breath, shift into a harder gear. That will let you go the same speed while peddling more slowly.
3. If your legs feel tired, shift into an easier gear.
4. If you see an "Oh my god!" hill coming up ahead, shift into your smallest chainring just as you reach the base of the hill. That will give you an easier range of gears so that you can climb the hill with dignity.
5. About twice a year, you'll have either a downhill or a tail wind that will let you benefit from the biggest front chainring. Make the most of those opportunities.
6. Whenever you change gears, whether front or back, you can pedal at the same cadence but ease up the pressure on the pedals so that the derailleur can finesse the chain onto the next sprocket more easily.