That's pretty much it. Don't make it more of a mystery than it is. In the beginning, leave the chain on the middle chainring (the "gear") in front, or the smaller one if you only have two, and ride around shifting just the rear gears, using the right shifter. You'll soon develop a feel for what that does. When you're comfortable with that, start experimenting with the front (left) shifter. "Soft-pedal" (keep the cranks turning, but without much pressure on the pedals) for a revolution or so when you shiftBlue CheeseHead said:1.) You must be pedaling to shift
2.) Larger gears (rings) in the front allow you to go faster, but is harder to turn. Good for flat roads and descents.
3.) Larger gears (cogs) in the rear make it easier to pedal and are useful on hills.
4.) Try and pedal such that your cadence (how fast you spin the crank) is in the 90 rpm range. Adjust to a combination of gears that will allow you to do that.
5.) Avoid having your bike in the big ring in front and big cog in the back or the small ring in front and small cog in the back. That is known as cross chaining and will put undue wear on the ring, cog and chain as the chain will be forced to operate on an angle.
Enjoy the ride.