Let's highlight the basics:
First, to set up an account with Twitter, as was mentioned you need an email account. Not a big barrier. It may take a couple days for Twitter's servers to actually see your account, though. Don't ask me why.
Then, you "follow" whatever accounts you want to, meaning you'll see what they "tweet" show up in your "timeline" (list of tweets from people you follow). Many of them will "follow back", meaning that what you tweet will show up in your timeline.
If you never tweet a thing, nobody will see anything from you in their timeline. No big deal. (Except that your account will look suspicious, as nobody will know anything about you.)
You can also "retweet" what you see in your timeline - meaning that it'll show up in other people's timelines as if you tweeted it (with original attribution intact).
But just because someone you follow has millions of followers, you don't automatically see what their followers tweet - just what it tweeted by the people you follow.
You will find new and interesting people to follow in any number of ways: others that you follow will retweet something interesting and you can follow the original account. You'll also find twitter accounts mentioned around the city - on advertising, websites, tv shows, menus, etc.
As has been pointed out, Twitter can be a useful source of information for whatever you're interested in: if you're interested in news, follow a number of news sources and you'll see a lot of news. If you're into sports, follow sports sources. Music? A number of musicians and bands will tweet. Reality shows? They love the attention, too. A number of MFC camgirls also tweet when they'll be online, so you can follow them if you wish. Hugh Hefner & his latest girlfriends also tweet, if you care. And so on.
Be aware, though, that the lists of who you follow, and of who follows you, are publicly available, so if you're following anyone you wouldn't want others to know about, then don't tell people what your twitter account name is. Or get a second twitter account.
Finally, although you can set up "lists" the default is for the tweets from everyone you follow to show up in your main "timeline" (i.e. a stream of tweets in chronological order). Most twitter clients (apps) will only look at the latest 300 or so tweets, so if you follow a large number of people, or if the people you follow tweet frequently, then you'll only see the latest couple hours, or the latest few minutes worth of tweets (again, depending on how many tweets there are). With the nature of twitter being very ephemeral that's usually what you want, so it's not a problem, and some sources (e.g. a lot of news and weather sources) will repeat the same content periodically so you can still read it. Skipping over content you don't care about it trivial. But if you want to see more, then you may have to take additional steps to get organized. Either way, twitter doesn't care if you check your timeline every five minutes, every five days, or every five months.
