When you are making a left turn at an intersection, you must always yield to oncoming traffic (vehicles coming straight toward you from the opposite direction) and also to any pedestrians crossing the street you’re turning into. Essentially, cars going straight (and turning right) from the opposite direction have the right-of-way over a car making a left turn.
So, if you’re waiting to turn left, you have to wait for:
All vehicles coming from the opposite direction that are going straight through the intersection (or turning right) to either pass or turn, unless you have a specific left-turn green arrow giving you a protected turn.
Any oncoming vehicles that are also turning right (since they can often make their turn without conflict, but be cautious – sometimes they may be turning into the same lane).
Pedestrians crossing the road that you plan to turn into. For example, if you’re turning left, pedestrians crossing the street parallel to the direction of oncoming traffic (basically crossing the street you want to enter) typically have a “Walk” signal when you have a green, so you must let them finish crossing.
In practice, at a green light without a green arrow, you would pull into the intersection (if legal in your state) and wait for a gap in oncoming traffic. You might only get to turn once the light turns yellow/red and oncoming traffic stops, or when there is a large enough break. Never cut in front of oncoming cars – that’s how collisions happen. If the oncoming car is close or going at speed, assume they’re not slowing for you.
In summary: yield to oncoming vehicles (they have the priority to go straight or right), and yield to pedestrians in the crosswalk. Only make your left turn when it is safe and clear, even if that means waiting through an entire signal cycle. Safety and the right-of-way rules demand that left-turning drivers be patient and let others go first.
