When there is a green light with a yellow left turn arrow. I was told by some people that if you're already in the intersection, you keep going and complete your turn but others say you stop. I'm meaning that the arrow was green when you entered the intersection, but turned yellow after you crossed the line. I know for a yellow arrow it says do not start your turn, but if you are already in the intersection does that count as already have started your turn or not?

Same as any other amber light, if you're already in the intersection you proceed with caution. So in your example you'd complete the turn if it's safe to do so.

Basically if you have already started the turning movement, keep going. Otherwise, if it has a circular green but the arrow has gone amber, you may enter the intersection but you must yield to oncoming traffic before turning.