With the new Twitter for Mac, you can easily tweet your photos on your computer by dragging it from Finder and dropping it to the tweet box compose window. The picture will be hosted by default at yfrog (which you can change from the preferences) and the character count will account for the shorten url of the image automatically.
You can also tweet using drag and drop from text and photos display inside Safari or Firefox. For text, just select the text you want to tweet and drag the selection to the tweet box. For image on web page, if the image contains a link, then the link url will be the text on the tweet box when you drag the image from the browser to the tweet box. If the image does not contain any link, then the image address url will be the text dropped inside tweet box. Instead of drag-and-drop to the tweet box, you can also drag-and-drop to the Twitter app icon on the dock to achieve the same.