Read this.

http://www.bikexprt.com/streetsmarts/usa/index.htm

What state are you in?

Basically, cyclists are allowed to make left turns just like a car. To do this competently, takes a bit of practice and experience (it isn't exactly easy). You have to move left earlier than you may be doing currently and you have to be able to keep tabs on traffic behind you.

Note that it's harder to do the left turn thing on high speed roads.

The better you get at making left turns, the fewer complaints you'll get from other drivers!