Clearly, my techno facility is pretty much limited to writing on the computer and looking for information on these internet tubes. I’m not a Twit, or whatever you call people who Tweet, so I don’t really know how the whole thing works. It seems like it’s a personal press conference for anyone who tweets. But what does it mean when someone asks - on a website, for example - to forward something via Twitter? Sometimes, what they ask to be forwarded exceeds 140 characters. And why do some articles have that little Twitter icon next to them. What gets sent where, and who sees it? Jeez, remember the telephone?
I hate the telephone. 
The Twitter icon is just an easy way to post a link to a particular article via Twitter. If you have a Twitter account and you click the Twitter icon next to an article, a window will pop up in which you can tweet a link to the article.
Forwarding something via Twitter typically just means posting it on Twitter. If it’s longer than 140 characters, I guess you could just post the link to it. Twitter has an automatic link shortening thing so that if you post a lengthy URL, it converts it into a shorter one so that it takes up fewer characters.
When you post something on Twitter, anyone who visits your Twitter page can see it. Additionally, anyone who is “following” you on Twitter will see the post show up in their personal feed.
And this means…?
It means that you post a link to the article from your Twitter account. “Tweets” are Twitter posts.
An example taken at random from recent tweets (I searched for “article” to find tweets where people were commenting on articles).
http://twitter.com/#!/designtaxi/status/182897206657949697
The shortened URL takes you to the article. Anyone who is following this person/company on Twitter will see the link to the article. So the more people tweet and share the link, the more people will hopefully read the article. That’s why websites want you to share links.
ok - two more: what’s the deal with “hashtags” and the @ sign? I hear people mentioning that all the time. Who cares and why? thanks.
Twitter usernames begin with @. If you put ‘@foo’ in your tweet, then that person will know you are talking about them, even if they are not following you.
Hashtags are strings that begin with #, like #straightdope. All these do is group individual messages together, so a person interested in reading messages about the Straight Dope might search Twitter for #straightdope, and they will see all the messages with that hash tag in it. It doesn’t matter where in the message you put the tag, so often they become part of the “language” of the tweet itself, like “I just read a really funny thread on #straightdope”.
You add the @ sign before someone’s username. It designates that the word is a username, rather than just a word (i.e. “I told @Munch to munch my munchies.”) It also then becomes clickable, so that you can go straight to that person’s Twitter account, where you can read their tweets, subscribe to their tweets, send them a direct message, etc.
The #, or hashtag, is a way to label your tweet. If I were to label my previous fake tweet, I might do this: “I told @Munch to munch my munchies. #food #directorders #Munch”. Each word with a hashtag also becomes clickable text, and will bring up a list of all tweets in all of Twitter with that same hashtag. Sometimes people will try to start hashtag trends. For instance, today it looks like one of the trending tags is “#Mets2012ThreeWordSlogans”.
@ is for replies. If I want to make sure that you’ll see a particular tweet of mine, I’ll use the @.
@CC Cheese it, the fuzz is here!
For people with lots of followers and people they’re following, their feeds can get pretty full. If I ignore my twitter feed for an hour, it will easily accrue 200+ tweets, and I don’t actually follow all that many people.
Hashtags are for searching. If I’m really into wine, I can plug #wine into the twitter search engine and it will pull out all the latest public tweets on the website that have the hashtag #wine in them.