To be honest when you're starting off, you might as well not bother with changing the gears on the left side of your handlebars. Just leave them in 2nd, which will select the middle cog on the front cogs next to your pedals.
You'll probably find then that you've got a pretty good range of gears by just selecting gears 1 - 7 on the right side (which will change which cog gets used at the back of your bike)
So assuming you've got yourself on the middle ring at the front (gear 2 on the left gear lever), when you first start off from stationary on your bike, you probably want to be in one of the first three gears on the right. As you gain speed, you can change up gears if you want until you get one that feels comfortable to you.
You may have noticed that you can't really change gears when you're stationary (or at least, if you do a horrible grinding noise is likely to come from the bike as you start off) so before coming to a stop, it's worth changing down your gears again to make things easy for yourself when you next start off.
Once you're happy with using the gears on the right, you can start using the ones on the left if you wish. The gears on the left 'adjust' the gears on the right, so 1st gear on the left makes all the gears at the right easier to pedal with (but slower) and 3rd gear on the left makes all the gears on the right harder to pedal with (but faster). This is how you get 21 gears - three versions of each gear at the back.
You'll probably find therefore that you can spend much of your time in 2nd gear on the left, except when you're going up hills (when you may prefer 1st gear on the left) or going down then (when you may prefer 3rd gear on the left)
I find when riding that I very rarely use 1st gear on the left, but then London is fairly flat. I tend to start off in second gear on the left, second gear on the right, then go up the gears as I speed up. If I wish to go fast, I'll normally change up to third gear on the left as I'm about halfway up the gears on the right, but the way you handle your gears is pretty much down to your personal preference.
Oh, and as mentioned above, don't select 1st gear on the left and 7th gear on the right, or 3rd gear on the left and 1st gear on the right, as it'll wear things down a lot more quickly. (Although don't worry if you do it now an then by accident - it's not going to suddenly break things, just wear them down if you do it a lot)