The way I learned about twitter is the same way that I learn about anything new. Usually I try not to look at the manual first, not because I think that I do not need the manual, but because I retain the material longer if I figure it out for myself. This is exactly what I did with twitter, so this would explain why I might not know as much about it as some other people who actually "read the manual" so to speak or why I did not tweet as much as others. The first thing that I always do is to go through all of the different tabs. For example there is a home, direct messages, favorites, and following tab.
I personally did not tweet very much because I really just liked to read everyone elses tweets; some of them can be quite interesting. Usually before every class on Tuesdays and Thursdays would be when I would read other people's tweets or occasionally write my own tweets. I never directed a tweet to a specific person because I was too busy reading other people's tweets or exploring twitter.
As a future high school teacher, I do not see twitter as much use to me. This is because twitter is different than a blog. On a class blog the students can only click on the things that I want them to, but on twitter they can write anything that they want. This is why I think that a class blog would be much better than a class tweet. At the high school age, more things than just school will be coming up in the students tweets and it would just put more things on me to have to make sure that they are only tweeting about apropriate school topics.