There's no set rule, you'll know by the feel of it, as you use the gears
more you'll get used to which one is best for you.  But it seems like you
may have already.  My rule of thumb is that if I'm paddling too easily then
I up the gear, or else my legs will tire faster.

Good on you!

Okay here goes... in basic terms...

Chainring at front - chain goes round it and at back of bike it goes round a
set of sprockets - you'll have seven on yours, so 1 x 7 = 7 gears. Basically
the smaller the sprocket at the back, the more your wheels turn for a single
revolution of the pedals, so the more effort required, but the faster you
can travel.

Small sprocket at back = high gear
Largest sprocket at the back = low gear

Hence - on flat or downhill when wanting to go fast - you choose a high gear
(small sprocket)
When you want to go slow or... you are going up hill and want all your
effort to go into getting you uphill rather than just turning pedals - you
choose a low gear (large sprocket at the back).

As a general rule - start cycling in a mid-range gear - and move up into a
higher gear. Lowest gears use for going uphill.

Of course, the more unfit you are, the more you use the lower (easier) gears
and the fitter you are the easier it is to use higher (harder to push)
gears.

Combine the above with cadence - the rate at which you turn the pedals. You
should be comfortable, on the flat at 80rpm as a rough guide and whatever
gear you are comfortable in at that cadence is most likely the right gear
for you in those conditions. Of course, if you go uphill, you drop gears.

Examples:-

My bikes each have 27 gears as a result of having a triple chainset at the
front (where the pedals are) and a 9-sprocket set at the rear as this is 3 x
9 =27. For everyday cycling I am usually in mid-range gears, that is I'm in
the middle chainring at the front and move up and down the sprockets at the
back. If I'm going up a steep hill (steep for me that is), I may need to use
the lower gears (formed by smallest chainring at front and larger sprockets
at rear) and if I'm on the flat and want to get a move on, I'll use the
higher gears (formed by biggest chain ring at the front and smaller
sprockets at the rear). I'm of the LA school of thought when it comes to
pedalling - going up any sort of steep hill (relative - steep for me is a
mere blip for a fit person...) I simply drop the gears and up the cadence.
That is much simpler for me than remaining in a high gear and pushing hard
to get up the hill. That wrecks my knees!

Think of it as car gears - you start off in a low gear and work your way up
the gears and if you have to go uphill, you go into a lower gear. Simple
really :-)

Cheers, helen s

Helen's answer was very good, but perhaps a lot of technical stuff to
absorb ...

In general, if you're starting out flat, you want to be in a gear that
you can pedal easily, and you want to pedal swiftly in that gear.
When you get to an incline, you can shift down (to "easier" gears),
and if you're going downhill and want to be able to pedal usefully,
you can shift up.  Ideally, you want to always be pedalling at the
same cadence (pedal strokes per minute), just in different gears
depending on the terrain.

I don't know if there are any real hills to worry about, but also, you
want to avoid "shifting under load."  That means that if you're
halfway up the hill and realize you really should be in a lower gear,
it's a bad time to shift; it's tough on the drivetrain.  The better
your timing in shifting, the quieter the shift will be.  If you're
approaching a short hill, go ahead and power up it without shifting.
But if you're approaching a longer hill, it's a good idea to downshift
before you start to struggle.

There are other considerations when you're not riding on pavement, but
I'll skip that until you start mountain biking =)

One thing -- when I started riding again two years ago, I also had
that feeling that lower gears were too "loose," but it's really that I
just wasn't used to it, and I ended up pushing too high of a gear.
Typically on a geared bike, you will want pedalling to be "easier"
than it would be on a single-speed.

I once again really, strongly recommend checking out the TE forums.
Chock-full of cycling advice for women.

http://forums.teamestrogen.com/

Nice!