- going to http://twitya.com
- enter competitor's twitter account, hit return
- see which users are replying or mentioning the competitor
- enter into a conversation with each one
- if they won't use or try your product, they might at least follow you if you give good reason, and are courteous.
- also see the friends of the competitor that you can follow too
- read the competitor's tweets
Some of my personal favorite stats are to watch people who RT more than once over a set time period about the competition.
"Like terms" is also handy because then you can add terms that are directly related but not identical to your competitor.
I'm sure that the big brand folks are already doing this and that there are paid tools ... but on a smaller scale, it's fast and easy to whip this sort of monitoring up.
The hard part is figuring out what these people want. You really need to have an insight into the weaknesses of your competition to accomplish that.