Here's an example of an intersection on my morning commute where I lane split. The yellow line shows the path I take.
There's usually a long line of stopped cars at the intersection, so I carefully ride between them to get to the limit line. I then move over to the center island and wait, taking off on the green light and heading to the second left turn lane. I usually am the first vehicle into the second intersection.
Cars see what I'm doing and seem to appreciate that I'm not interfering with their attempt to get through the intersection or turn left.