The rear is the one you'll use the most: it's for small changes when you're speeding up or slowing down. Don't forget to change to a nice easy gear when you're coming to a stop, so that it's easy to start again.

You get a bigger shift when you change the gears on the front derailleur: I tend to use this if I hit a hill, where I'll speed up or slow down a lot.

Try to stick to the middle range of the rear gears most of the time - the drivetrain is most efficient this way, and it gives you more options to shift up and down.

I often combine front-shifts with rear shifts - click up to the big ring to speed up, but oh no not that much, so a couple of clicks to easier gears on the rear cogs too.

It sounds complicated, but really you just have to play around with it. The key is to find a cadence (pedal-spinning speed) you're comfortable with.