I suppose the “why” part is important too. You can Google the title of this Discussion, and what you’ll currently find is a lot of “What Bands Should/Shouldn’t Do” lists regarding Twitter tactics. (These are actually pretty good resources and contain solid ideas for the most part. Go check them out if you’re sold on the “yes” answer.)
The overarching reason that you should be on Twitter, succinctly put, is because it is a magic serendipity machine.
Forget about getting followers; put aside the fantasy of having 60K followers and getting RT’d like gangbusters (hint: lots of followers is the result of success, not necessarily the thing you need to achieve to become successful).
Every single tweet is like a tiny lottery ticket. You never know where it will lead or who will see it or act upon it. You can improve your odds by using Twitter for the express purpose of trying to cause serendipity.
People call this “making your own luck.” It’s a very real practice.
Try tweeting at a booker, or an agent’s friend. Ask people who tweet about you or about your genre to come to a show, if they’re from the area. Take the time to truly try and talk to people (and move it off Twitter if the 140 limit becomes cumbersome) instead of worrying about creating content, getting RTs, following, unfollowing, etc.
You’ll be amazed at the magic that can start from a single tweet. You’ll be amazed at the amount of people who are willing to chat for a bit. You’ll be amazed at how some of those people can seriously impact your career.