Karen Tumulty has a good story about the way that twitter is working in the 2012 campaign so far. It's especially useful, I assume, for those who don't really have any idea about what twitter is and how it works within contemporary campaigns.
The only problem is that it's a bit of a mishmash. I'd put more emphasis on a divide between twitter as advertising, which I suspect isn't really much of a big deal, and twitter as public communication within the parties and between the campaigns and the press.
It's that latter one that I think is definitely worth knowing about. I doubt that the mass advertising function of twitter will be a significant factor in any campaign at this point. But how elites -- interpreted very broadly -- communicate can be a big deal. There have always been ways that such communication happens, whether it's the partisan press of the 19th century, or the Sunday talk shows of the mid-twentieth century. Presumably, however, changes in the medium do in fact make some sort of difference to what's done. For example, there's the question of just how public such things are; there's also the question of how participatory they are. What's interesting about twitter is how participatory it is compared with, say, Meet the Press. Now, I wouldn't go too far; there's an illusion that anyone can participate in the conversation, but for the most part that's really just an illusion.
I'd also note that the back-and-forth between campaigns, along with the efforts to get something to trend, resemble in some ways the old trick of running an ad only on Washington TV channels in order to create the illusion that the whole nation was seeing it. The trick, veterans of 1980s and 1990s campaigns will recall, was to get the press to report on the ads, thus amplifying the message far beyond what a campaign could afford. That's pretty much what happened with the Hilary Rosen thing, no?
At any rate: you pretty much have to use twitter if you want a good sense of the campaign as the campaign professionals perceive it. Which is not to say that you have to use twitter; you're not going to learn more about which candidate to vote for, nor are you going to learn more about who is going to win. But if you want to know the latest campaign developments, that's certainly the way to do it this time around.
(Oh, and while I'm at it: shouldn't you be following me, already?)