Left turns at controlled intersections are one of the most dangerous driving maneuvers. They don't have to be -- the dangers can be controlled. The most important thing is to be knowledgeable -- and then MINDFUL -- of what they are.
When you enter an intersection, the immediate danger is the traffic coming from your LEFT on the cross-street. Look left first, to make sure all traffic is stopping before you enter the intersection. Look left first, then right, then left AGAIN before you roll into the intersection. A red light runner is going to arrive, on average, within four seconds of the light change. You don't want to be there if he does.
Pull into the intersection (unless the law in your state dictates otherwise), but leave room for left turners coming the opposite direction to do the same. Modernized intersections have off-set opposing left turn lanes, so that both directions have a good view of the oncoming traffic. Some driving instructors will tell you NOT to enter the intersection until it is clear to turn. I disagree. The greatest danger in entering the intersection is the red light runner -- and after the first four seconds that danger largely evaporates. Sitting behind the crosswalk prevents others from making their left turns on that light cycle. This is unnecessary and holds up traffic flow.
Once you're out there, yield to all oncoming traffic. In my state, the left-turner must yield to ALL oncoming traffic, even if they run the red light. This is because the left-turner is almost always the last person with the opportunity to avoid collision -- since he is typically sitting still, waiting for the traffic to clear. If you do not have a clear view of the oncoming traffic, in all the lanes, then don't begin your turn. When you see that all traffic has stopped, then you can go. I am amazed at the number of drivers who gamble everything they have by making BLIND left turns. I've watched some of them die. If you think about how most people view yellow signal lights ("time to hit the gas"), you understand the dangers!
Don't turn your wheels in the direction you are turning until it is clear to go. If you are rear-ended while you are waiting, your already-turned wheels will guide your vehicle into the oncoming traffic -- so keep them straight until the way is clear to complete your turn. Then, complete the turn into the correct lane.
One last hint -- if the traffic is heavy, the left-turn lane is crowded, and it looks like it will take more than one light cycle to be able to make a left turn, consider continuing through the intersection and make three right turns instead. If you do this on side streets (not private property) it's legal and often quicker (when traffic is congested).
Keep it between the fence posts!