I expect you've seen this forum post.
The instructions were accurate at the time (2 years ago) but things have changed slightly since then. (There are now certain files that are shared between all themes.)
If you've already put your 'favicon.ico' file in your root directory (not necessarily the same as your Showkase root directory) and it's not being picked up by your browser, then add the following code to your 'showkase/_themes/base/pagetypes/basetheme.tpl' file in the {block "stylelinks"} ... {/block} section between lines 27 and 30 (alongside the other <link> tags.
<link rel="shortcut icon" href="/favicon.ico" type="image/x-icon">
You can change the location of your 'favicon.ico' file if you like (it does not need to be in your root directory) but just make sure that the path to the file is correct in the 'href' attribute of the <link> tag.
Be sure to publish your site afterwards (just click the 'Publish' button) to have this <link> tag inserted into all your pre-existing Showkase pages.
Please note that the file and line numbers above refer to the current version of Showkase (v1.6.1).
If you are not already using the current version, then you might like to upgrade your site following the instructions here.
For a list of changes between versions, please see the Version History.
Incidentally, once you've posted a couple of posts, you should hopefully be able to include links. (Otherwise, you can disguise the links by inserting spaces between slashes or leaving out the http:// part.)