You can find a quick wizard on twitter's site to add a twitter widget onto Myspace, facebook, blogger, Typepad or just a regular HTML/Flash widget (see related links below).
If you want to show a twitter button so people will share your page through their status updates on twitter you can use services like Pagecodes.net or AddThis.com
You can also find many twitter plugins for wordpress and probably other blogging platforms. There have different design styles and functionality. Choose one that works for you the most(systematically and appearance-wise).
If you don't want to put that much effort you can always just show an image/icon associated with twitter and have it link to your twitter profile page.
There are some great sites to copy and paste the code for a twitter button - try www.pagecodes.net for starters - those creative geniuses among you can design your own image and apply it to the code.
If you Google "add twitter buttons to my site" you can find various sites that have twitter buttons, one of which is twitterbutton.com . You can choose different icons and then get the HTML code and put that code onto your website.
You cannot use the website icon on the desktop. You can always add the bookmarks, which are same as icon of page.
The Twitter icon is a little blue bird. Presumably they used a bird as they 'tweet'
you would have to embed the picture and create it with a hyperlink
Tjetz is a famous twitter icon .
Twitter allows for a small square icon to be uploaded and that's all that's built-in. Google will yield a number of sites designed for uploading pictures to twitter and most of them integrate pretty well. try http://twitpic.com/
Your header is the picture behind your icon and bio. (Your icon is like your profile picture)
Save a gif to your computer and upload it as your profile picture on Twitter.
You can't copy and paste images on Twitter.
You have to be a translator and contribute to translate parts of Twitter into other languages.
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If you have a custom icon you can simply upload it where you would normally upload your display picture.
Tweeting can be done on the Twitter website.