Nothing seems more intimidating while driving than using a roundabout or traffic circle for the first time.
I remember when my young son, who was 14 at the time last year, approached a traffic circle for his first time. I had to quietly talk him though it. We did it three times before he developed enough confidence to do it without my commentary.
It seemed like there was so much to do: am I in the correct lane so that I can get to the road I want to get to without causing chaos for the other drivers in the circle; turn signals - left-right-when-where; entering and exiting the circle; yielding to vehicles already in the circle; breaking into the circle traffic to get to the left lane; impatient people behind you; drivers going too fast in the circle; drivers not following the rules; and on and on.
In cities like Edmonton Alberta or Calgary Alberta, there are usually two lanes going into the traffic circle and two lanes going around and rules for each lane you are in. The instruction signs go by too quickly or are not noticed due to the amount of traffic or pedestrians to watch for, so new young drivers get a bit panicked. A traffic circle is usually quite large in diameter as opposed to a roundabout which is usually quite a bit smaller and usually one lane.
Before we go into the stats showing why roundabouts or traffic circles work so well, let's drive up to a traffic circle and enter the traffic flow.
As you approach a two lane municipal roundabout, usually called a traffic circle, signal your intentions by using your turn signals. This is extremely important because other drivers behind and beside you can't read your mind. Yield to traffic already in the circle. Let's say you are approaching a traffic circle with four roads entering it which are roughly 90 degrees apart. You are in the curb lane of a four lane street with two lanes same direction each way. You may signal right and then after giving way and entering the traffic circle, take the first street to the right. Or, to go to the second street, you may signal left when entering the traffic circle and, after passing the first street and changing your turn signal to indicate a right turn, go to the second street and turn right.
If you want to go to the third street, then be in the left lane before entering the traffic circle and when entering the circle, with your left turn signal on, start around the circle, passing the first street and the second street, and then put your right turn signal on and turn on the third street, staying in the proper lane while doing so. Sound confusing? Then go to this University of Alberta web page for very good pictures and explanation of traffic circles in Edmonton.
Summary:
When approaching the circle:
1. yield to the cars that are already in the circle
2. enter the circle from the right lane if you intend to go "right" (first exit) or "straight" (2nd exit)
3. enter the circle from the left lane if you intend to go "straight" (2nd exit) or "left" (3rd exit)
REMEMBER: SIGNAL IN, SIGNAL OUT
Also watch this video which is on the Alberta Transportation website. It has to do with single lane roundabouts, but the concept is the same.
Finally, from the Alberta Drivers License Handbook, and mentioned at a calgaryarea.com web page we have this explanation, which is directly from that page.

Traffic Circle
In a traffic circle , the vehicle on the right must yield to the vehicle on the left. The driver on the left must signal and use caution when leaving the circle and crossing through the outside lane.
In this diagram:
B and C must yield to A.
E must yield to D while F and D proceed together.
H must yield to G.
Traffic in the lanes indicated in red , must yield to traffic in the lanes indicated in yellow. Traffic entering into the circle must yield to traffic already in the circle. when you are leaving the traffic circle use your right turning signal to warn other drivers of your intention.
Ok, one last tidbit. Safety stats from the Alberta Transportation web page mentioned above.
When compared to other types of intersections, roundabouts have a demonstrated safety record:
* more than 90% reduction in fatalities
* 80% reduction in injuries
* 40% reduction in total number of crashes
You do get used to roundabouts or traffic circles. I, for one, like them. They are convenient and it beats sitting at traffic lights, when you can be around and gone in just a few seconds.
So, if you are new to traffic circles, try getting used to them at low traffic volume times.
Good luck - Drive safe...
Cheers - Mike