Before digging into the meat of the Maya-to-Qt discussion, I should probably cover some basics first.
Because all of my Maya/Qt work is currently happening at Reel FX (as I still don't have a current version of Maya at home for various reasons), everything I do will be based on the software versions installed at Reel FX. As of this writing, we're using PyQt 4 with Qt 4.4.2. Most of my work at this point is with Maya 2009. While we do have later versions available, and I may make occasional reference to idiosyncrasies in those versions, assume for the most part that this is all happening in Maya 2009.
One thing that I definitely won't talk about in these posts is how to install either Qt or PyQt, or how to get PyQt conversing with Maya in versions prior to 2011. I'm avoiding that hurdle largely because it was cleared for me by the folks at work, so I don't have any hands-on experience to share in that regard. If you want, head on over to Nathan Horne's blog, where he has kindly shared some packages that he put together to make the PyQt installation process a little easier. I haven't personally used those, though, so I can't offer any comments on their effectiveness.
While the code samples that I list will be (ideally) fairly complete, I may only present partial code pieces here and there, partly because I'll be pulling some of these examples from actual stuff I'm doing at work. Those omissions are not only to address code-proprietary-ness issues, but because of some customizations that were done to unify all of our Maya/PyQt development at Reel FX. Just be aware of that in case you copy-paste any code samples that you find here. I'll leave in the essential stuff like imports, naturally, but some other parts won't be there.
I think that about covers it. In the first post (coming soon), we'll take a look at Qt's signals and slots, and then delve into meatier UI topics from there.