To "install" this add-on simply go to Mozilla.com and search for TwitterBar.
A small Twitter icon will be located on the right of your address bar. You post your tweet by clicking on it. If you want to see how many characters you have left, just hover your mouse over it.
Clicking the Twitter icon when visiting a webpage will send a tweet containing the URL of the webpage you are currently viewing. You can adjust if you want some pre-text to show up in your tweets sent this way.
For example, if you are on Google homepage and you click the Twitter icon, it will send a tweet like: “Currently Browsing: [link to google homepage]“. Of course, the pre-text can be disabled and you can write whatever you like instead.