Go to Twitter.com (and log in if needed). If this is a new account and you have not tweeted yet, you will see a message about getting started before the tweet editing box:
If you include a link, paste in the complete URL, and Twitter will automatically shorten that for you. As you type, Twitter will show you how many characters you have remaining.
NEXT STEP => You are now tweeting! Next, you will follow some people, and you will see their tweets too!
About those 140 characters... As with text messaging, the strict character limits at Twitter have spawned all kinds of acronyms; you can see a few listed here: Twitter Lingo Cheat Sheet. :-)