Who do you yield to?
Technically when you are turning right on a green light, the only people you normally need to yield to are pedestrians and cyclists. (Of course, you may need to yield to someone else – such as a left-turning vehicle, if it has already turned and is subsequently in your way – however left turns are supposed to yield to right turns in this situation.)
Try to move your vehicle closer to the curb before the right turn so that vehicles behind you can fit by in case you do stop for pedestrians. Before you move over, use a right-mirror check and/or right shoulder check to ensure there are no bikes that you would be potentially in conflict with. If there are no pedestrians and any left-turning vehicle is clearly yielding, then simply turn.
If you see pedestrians, move forward into the intersection a bit in order to line up your vehicle with where you are about to turn. There are two reasons for this: it clearly tells the driver of any left-turning car that you are seriously getting ready to turn right and you are merely waiting for the pedestrians. If you wait behind the white stopping line, the driver may think that you want him/her to go first, because it looks like you’re leaving an insanely large amount of space in front of you for no reason (keep in mind, there should be no pedestrians walking on the perpendicular crosswalk; so it’s fine to block it). The other reason has to do with the traffic light. If you move forward into the intersection, wait for slow or many pedestrians, and then the light goes yellow, then you’re still allowed – and you should – exit the intersection after the pedestrians, but before any left-turning vehicle.
More on pedestrians & positioning
Give the pedestrians some extra time before you turn. You don’t have to necessarily wait until they’ve walked completely across the entire crosswalk (in certain intersections, that might mean waiting for them to walk past multiple lanes, which would be silly). Usually you should wait until they’re at least past the yellow line if they’re walking away from you, or until they actually step onto the sidewalk if they’re walking toward you. Do another quick shoulder check before you turn to make sure there are no more pedestrians about to walk.
The oncoming left-turning vehicle
Do keep an eye on the left-turning vehicle. If it turns when it shouldn’t, then simply let it go first and go after it.
If there are two lanes, then avoid turning at the exact same time as the left-turning vehicle. You need some extra space around your vehicle at all times and turning at the same time robs you of this safety cushion. Try to time it so you turn before it or after it, but not simultaneously.
Which lane should you turn into?
Legally when you turn right, you’re required to turn into the right lane; and any left-turning vehicle is required to turn into the left lane. However, if after you turn there are no vehicles in the other lane, you can quickly change your turn signal to a left signal and make sure it is safe and do a lane change into the left lane fairly quickly. This is perfectly legal as long as 1) you are not crossing a solid white line and 2) it is safe (obviously) and 3) your left-turn signal is flashing.
Yellow traffic lights & right turns
*By the way, if you’re approaching the intersection for the right turn and the traffic light goes yellow, you are legally required to stop behind the white line and yield to others, unless it is not safe to stop. See Right Turns on Red Lights for more info.
There seems to be a lot of confusion about yellow lights. If you are just driving along and your light goes yellow, it means “Stop” unless you can not safely stop in time (ie if you are “past the point of no return” or if it is not safe to stop). Why would you not be able to stop in time? If, by stopping, you think you would risk being rear-ended because the vehicle behind you is too close then you should keep going. However, if you get into a collision you must prove that it was unsafe to stop for your yellow light. And I’m not sure how you would do that, so it is best to avoid speeding, anticipate traffic lights changing and be prepared. Check your rear-view mirror well in advance of the intersection.
If you are turning right or left at an intersection, the same rules apply. If the light goes yellow on approach then you should stop behind the white line as long as it is safe to do so. Yes you may be able to turn right on a red light, or left on a red light if turning onto a one way street, but you MUST STOP first if you are facing a yellow light or a red light and yield to those with green lights.
If you’re turning left or right at an intersection and you have already entered into the intersection when the light was green, and then it changes to yellow, then it is a different story; you must then clear the intersection when it is safe, regardless of the traffic light colour.
How can you tell if the light will change to yellow soon? See this post: How to tell if the light will change soon