I generally use a four-prong approach:
- Official documentation
- Source, if available
- Google based on keywords, often with site:stackoverflow.com
- Blogs
The order of these options changes depending on the type of questions I have. If I'm looking for information on a method signature or what properties a class has I'll look at official reference documentation first. If I want to know how a class works, I'll check the reference documentation if it has good examples, but often will go directly to the source when available. This is especially true if the software is new or the documentation is poor. I use the source for ASP.NET MVC a lot since the documentation doesn't have examples yet. I also use the source a lot for jQuery plugins whose documentation can be very hit and miss.
If I'm looking for techniques rather than references, I'll usually go the Google route or look at blogs where I know that the author works in that area. I don't follow a lot of blogs, so that option is rarely used except for specific technologies -- like ASP.NET, MVC. Google can also be hit and miss, though I'm finding that much of what I need is now available via Google on StackOverflow. I've never really had much luck with the SO search functionality -- sorry.
My option of last resort is to ask around -- say if it takes me more than an hour to find any meaningful help on the web. This is probably unique to my situation since most of the other developers I work with work in different technologies. When I'm out of my element, working in one of their technologies this is often my first option.