Dealing with colleagues avoiding work I doing a PhD in a research group where there are 4-5 PhD student and 1-2 Postdocs. Given the nature of the research projects, more than one person ends up working on one project and sometimes people work on multiple projects simultaneously. 

I am assigned to work on a project where a postdoc is supposed to help me. Recently, a deadline arose and we had to submit a project in two weeks which was extremely tight. I am the principle person working on the design, but given the tight deadline, my advisor asked the postdoc to help complete the design. The design consisted of two parts which were simulations and drawing. I was working on the simulations which were time-consuming. I asked the postdoc to learn how to use the tool needed to draw the design and then teach it to me quickly at before the time of submission so that I do not have to go through the user guide as time was tight. He refused just after the meeting where my advisor asked him to help me saying that he will not draw anything. In the meeting, he seemed fine with helping me.

Given that I was very eager for this project to succeed, I pushed myself and completed everything on my own with no help. I submitted the design successfully. 

Now I am considering telling my advisor what happened. This person is blatantly avoiding work and try to dump everything on me. This pattern of behavior has occurred more than once before. We are understaffed in this project and I cannot carry it on my own. At least three students are needed and now it seems that I am on my own. 

My question is: What would be the best way to tell my advisor about this postdoc? I do not want him to get the impression that I am whiny, but I believe this is an issue needs to be addressed and that a more professional behavior is expected from the postdoc. What things should I avoid in explaining this problem? Is telling him about the issue going to help with anything?
Try this: "Professor Smith, I'm glad we met the deadline, but I think I should tell you that I ended up doing all the work myself.  I had asked Bill to get up to speed on the drawing tool so that he could jump-start me when the time came, but he didn't.  Perhaps next time, you could ask us to develop a plan for partitioning work, which you would then approve."

You've let him know what happened.  More importantly, you've suggested a way to prevent such problems in the future.  It's a solution that doesn't require much of the professor's time, either.  (And, if the "approved plan" doesn't work, at that future time you could suggest progress reports from each team member.)