There's a saying among flight school operators - "We charge $100 to teach you how to fly, and $10,000 to teach you how to land!" 

There's some truth to that, and the fact is that in the early days you will spend a lot of time in the circuit. You'll spend time there later as well, keeping your flying skills sharp and practising your take offs and landings.

So, what is the circuit? Simply put, its the pattern that pilots fly around an airport when they're practicing.  If you think about it for a minute you'll see that it makes sense for the practice pattern to be a consistent and agreed upon  pattern, just from the air traffic point of view.  And that's exactly what happens with the circuit.

The circuit consists of five parts, called "legs".  Starting on the runway you do the "take off leg", wherein you take off and begin climbing to circuit height.  Circuit height is normally 1000' above ground level (AGL).   You don't get to 1,000 AGL on the take off leg, however.  Instead, what you do is take off, doing your ground roll procedure (full power, gauges green, airspeed alive, rotate) climb through 200' and do your checks (again, full power, gauges green, airspeed alive, but this time add positive rate of climb), and then, usually at 500' you make a 90 degree climbing turn in the circuit direction.  

The second leg is called the "crosswind leg", and it runs perpendicular to the runway.  In most planes you'd climb to 1,000 in the crosswind, but in my 150 I start my turn out of the crosswind at 800', since it climbs a little slower than a C-172.  Its a good idea to take alook around before you start the turn out of the crosswind leg.  

The third leg is called the "downwind leg", and it runs parallel to the runway.  The downwind is where you do the pre-landing checks -mine go from left to right (primer in and locked, masters on, mags both, fuses/breakers ok, carb heat hot, gauges green, fuel both, harnesses and doors secure, brakes tested).  Once that's done you make the call to the tower. Listen and make sure the frequency is clear.  If someone else is transmitting let them finish, wait for tower to respond, listen for the other pilot's reciept confirmation, and then make your call ("Tower, this is Whiskey Juliet Charlie on the downwind for a touch and go on 26 left" ).  Tower will respond and tell you that you're first, second, third or whatever, and will advise you of traffic.  You must respond to them, and if they tell you about traffic you either tell them you see the traffic ("Whiskey Juliet Charlie with the traffic") or that you don't ("Whiskey Juliet Charlie looking for the traffic").  You need to know where  the other pilots are so you don't crash into them, so if you say you're looking for them, look.

Assuming you have the traffic and know what order you're going to land in you can start getting ready for the next leg.  Slow down, apply flaps, and follow your normal procedure. If you've seen the traffic and its past you, and if you've got the end of the runway at a 45 degree angle to a point between the end ofyour wing and he end of your elevator, you can make another 90 degree turn into the "base leg".  

You continue in the base leg until you are ready to turn and line up with the runway.  In my plane I wait until the end of the runway has just passed the end of my pitot, and then I start the turn.  During the base leg you usually are descending as well, ideally on the right glide path and at an appropriate power setting (that varies with temperature, wind and the length of your downwind leg).

The fifth part of the circuit is the "approach leg".  You line up the runway, set up the glide path, set the power and maintain speed by the attitude and rate of descent through power.  In good conditions it's easy, but wind can make it more interesting.  As you're lining up the cowl rivets with the runway the tower should advise that you're cleared to land ("Whiskey Juliet Charlie, you're cleared for a toouch and go on 26 left" or something very similar).  If you don;t get the clearance you have to call tower and ask for one, or else you can't land.  

Normally when you're doing the circuit you're doing a touch and go landing, so you get your clearance, touch down, and finish the approach leg.  You raise your flaps, check that they're coming up, try to stay straight on the runway, apply full power, transition to the take off leg, and repeat the whole process.

So, five legs: take off, crosswind, downwind, base and approach. 

Most circuits are left hand, meaning you turn left into the crosswind leg, and then continue to turn left.  That can change from airport to airport, and can change at an airport.  If circuits are usually left hand ones at your home airport they can change to right hand circuits.  In fact, they can change to right hand circuits while you're in the circuit.  If that happens you have to imagine the left hand circuit being drawn on paper, then imagine where the right hand circuit would be in relation to it, and then make the change as directed by tower to the right hand circuit (its not as hard as it sounds if you just follow the directions).

Sometimes tower will tell you to start your turnout (the change from take off to crosswind) early, or to extend the downwind, or to turn base when they advise.  Follow their directions.  They're doing that to help space the traffic.

Try to keep the circuit shape consistent, with square, rather than angled corners. If there is a crosswind you'll have to crab a bit.  Maintain circuit height as accurately as you can. 

That's flying the circuit.  Remember, the circuit exists whether you're flying it or not.  That means that it's there when you take off to go somewhere else, and it's there when you arrive from somewhere else.  In other words, you either leave or join the circuit whenever you come to or leave the airport.  Keep that in mind, remember how (or find out) the circuit at the airport you're at works, and join it as instructed.  You really don't want any fender benders in an airplane!