You can also save arbitrary sequences of Unicode in the chart view, such that the optional toolbar icon (drag the extension's icon (an image of a "U") to one of your toolbars via View->Toolbars->Customize) can be used to paste these snippets of text into Firefox or web pages. Use right-click to remove an item.
Use control+left-click while you are hovering the cursor over the chart view to freeze the descriptions below. See help in dialog window for more nuances.
You should be able to download the Unihan database (not included with the extension due to size) from within the preferences. If you have trouble, download the approximately 25MB file from http://bahai-library.com/zamir/Unihan.sqlite and place it in your Firefox profile directory.
Please be aware that in the Unicode chart view, items like question marks (Firefox 2.0) or boxed numbers (Firefox 3.0) may appear in place of a desired character (and some characters will not or cannot be displayed at all). This is due to the available font's own present limitations in displaying such characters. To find these, you could consult the images such as those at the official http://www.unicode.org/charts site, now also accessible through the extension. While in the extension, you can hover your mouse over a character from the desired range, and a link will appear which you can click to lead to the appropriate chart and optionally view the image.
Web developers can also use this extension's "x-unicode:" protocol to link in a generic way to a Unicode character (which this extension will use to open the chart dialog). Other extensions or Unicode applications are welcome to collaborate to develop and propose a definitive standard. See http://brett-zamir.me/tests/unicodeProtocolExamples.html (will only work with the extension installed).
The Unicode data within this extension is licensed as described at http://unicode.org/copyright.html
Translators welcome at http://www.babelzilla.org/index.php?option=com_wts&Itemid=88&extension=2979&type=lang