Plan well in advance for a left turn on a busy street. Glance back repeatedly until you find a break in traffic, then signal and cross over to the left turn lane. If you can't find a comfortable chance, just go straight and stop at the corner. However, instead of riding in the crosswalk (illegal in Los Angeles and most of the county anyway), ride just to the left of the crosswalk so you're technically part of traffic without impeding the cars.

+1 to common sense and intuition.