You don't need a link (meta tag) unless the following criteria are not
1. The file is 16x16 pixels
2. Its format is ICON (not something else renamed to .ico!)
3. The name is favicon
4. Its location is the site root (.../public_html/) equal to HTML /
Summary: /favicon.ico . If any of these are not met, you will need to use a meta tag.
If you think you have it in the right place, enter http://yourdomain.com/favicon.ico
, and it should display in your browser. If it doesn't, check if you have .htaccess redirection sending requests for /favicon.ico off to somewhere else. The only remaining possibility is that the file was created with the wrong format.
Note that if you add or change the favicon on an existing site, it may take a few days for your browser to get around to asking for a refresh of the favicon (it seems to depend on the particular browser). You might be able to prod it into doing so by removing the site from your bookmarks/favorites, clearing the cache, and loading (and saving) the page again. You can also ask someone else to try your site to see if they see the favicon.