Crast

You have to merge left much earlier than when you reach the intersection. If there are several lanes to get across, you'll want to give 100-200 feet for each lane you change, possibly more based on traffic speed. (and getting from the shoulder/bike lane into the right lane counts as a lane change) If there's already a bunch of cars waiting at the light, you'll want to shift even earlier so that you're in the correct lane when you catch up to the car waiting in front of you. You definitely do not want to cut a diagonal / perpendicular to the direction of traffic, it's awkward and people won't be expecting you. The right distance you'll start to get for each intersection.

It will get easier. Generally I'm moving slow enough (coasting or softpedaling) when I approach the messier intersections that if I feel I need to and I don't have a place to merge, I'll coast and wait for the light to turn red, and then people aren't rushing to get to the intersection and may give you more space. But this isn't usually a problem.

When there's no left turn lane, and the light is red, I'll just get behind the last car in the leftmost lane, taking the whole lane. On particularly fast approaches to such an intersection (such as if it's downhill) I may take the lane much earlier, like at the top of the hill, to prevent having to merge at 30+mph.

If I'm not turning at an intersection and instead turning left into a complex or shopping center, etc in the middle of a road (which I do to get into my subdivision from a 50mph road with one lane in each direction) I get closer to the double yellow, but not on it or crossing it, because I do not want to be whacked by an oncoming driver. I put out my left hand well enough before just like I would if I were in my car making that same left, then put my hands on both brakes, slow down and then as I'm just rolling to a stop, put my left hand out again, putting my foot down if I have to stop. I also usually quickly dump 2-3 gears on my casette as I roll up, so that I have it on an easier gear which gives me a faster jump.

I am lucky to live in an area which has many quieter residential roads to choose from as well so I can avoid a lot of the ugly roads. We do have a lot of busy high speed roads, but those tend to have intersections miles apart, so for the few icky intersections I have to deal with, I've already worked out the protocol. If I ever had to deal with an intersection I was not familiar with and I couldn't immediately figure it out during the approach, I would probably fall back to dismounting and walking the crosswalk. Figure out your own intersections, and if you can, try and find alternates to replace the particularly ugly ones. The biggest battle is just knowing your territory. visibility (such as coming around curves, over hills) angles, traffic speed, tendency of people to run lights, the timing of the light changes is all important. Changing lanes earlier might mildly irritate people, but it's better doing it before than after a blind corner where you don't know if someone will come up behind you and change lanes.