I guess it comes down to confidence, and it may take a while for you to build that. Building strength will also help with the speed neccesary to negotiate traffic. Judging the intentions and speed of the traffic is also a learned skill.
But your job is to signal your intentions, if turning -- especially left -- and make your move accordingly. If you are approaching an intersection and intend to turn left across multiple lanes to get in the left turn lane, you need to be doing that with plenty of distance to spare. Once you are over, hug the right side (which will often have a barrier), then take the lane in the line-up, like any other vehicle.
For going straight through ... there's nothing to it. Just proceed. If you can easily reach the walk signal, sure, give it a push.
A rear view mirror helps, but also shoulder check; it's more reliable to judge distance.