Nice one smudgely, you'll easily be ready for that challenge next year at this rate.
Re gears, rh100 has done a good description. It's generally easiest to remember that "low numbers are easier to pedal; high numbers make you go faster" - at least that's how I explained it to Little-LC.
So the left hand shifter will move the front gears: you might have 2 or 3 of these. Number 1 will be the smallest (leftmost) ring at the front, then 2 then (maybe) 3.
The right hand shifter moves the back gears: you'll have somewhere between 5 and 10. Number 1 is physically the biggest ring (leftmost) at the back, then numbered left to right to the smallest.
As rh100 said, the back gives you smaller "steps" between gears whereas the front is big steps. The idea is to keep your legs moving at a speed where they feel comfortable: somewhere between 80 and 100 turns of the pedals each minute is generally reckoned to be a good figure to work with. I find around 95 is most natural feeling for me. How fast your legs are spinning round is what's called "cadence" and it's measured in revolutions per minute.
So, my bike is a mountain bike and has 24 gears: 3 at the front x 8 at the back. This is how I use them to go to work ..
Most of my riding to work is done using 2 (middle ring) at the front and somewhere between 3 and 6 (sometimes 7) at the back. I tend to start off in 2 at the front, 3 or 4 at the back. After half a mile or so, I come to a steepish hill and I know I'm not gonna get up it in the middle ring so just as I start the "bigger" climb I change down to 1 at the front: I'll already be on 3 or 4 at the back, depending on how the lower part of the climb has gone.
The combination 1-3 will normally see me up the hill. Sometimes I go for 1-4, sometimes 1-2, just depends on how my legs feel. Spinning a lower gear round fast is easier on your legs, but makes you breathe a lot harder.
At the top I go into some woods so I generally stay on the granny ring and use 3 or 4 at the back. Sometimes I go up to the middle ring and run 2-3 .. it just depends.
Once I come out of the woods, I start to go downhill and join a road so I go onto the middle ring (if not already there) and quickly work up through 3, 4 and 5. Then I tend to use 2-5 or 2-6 to cross the first housing estate I pass, all on road.
As I leave that estate, I'm on a slight downhill for a couple of miles: it's a bridleway that's been kind of co-opted as a ped / cycle path for a bypass so it's well surfaced and wide, with hardly ever anyone on it (they're all in cars in the queue on the bypass
) so with the downhill and (usually) a tailwind I go to the big ring at the front and use 6,7 or 8 at the back to move a bit faster.
That's what works for me: I tend to use the front to be in the correct "range" of gears for what I know is coming up, then "fine tune" at the back.
As rh100 said, you should avoid "cross chaining": if you're on 1 at the front, don't use your highest numbered few gears at the back, equally don't use the lowest numbered ones at the back with 3 at the front. If you do, the chain runs at quite an angle between front and back and it don't like it!! There will be another gear using a different combination front-back that is about the same.
I generally use 1 to 4 at the back with 1 at the front, 3 to 6 (sometimes 7) at the back with 2, then 6 to 8 (sometimes 5) with 3.
By the time you don't use the "crossed" gears, and allow for combinations that are close to each other you find your number of useable gears is much lower than the number of gears you have. I typically use 10-12 at most of my 24, and there's 8 combinations that I use 80% of the time.
A long post, but I hope it helps.
I just play pot luck with the gears, but I really don't know when I should be changing gear, I seem to just change when I *think* I should rather than when I need to or I will change when my legs hurt..... I need a lesson on gears. 
