There are basically three ways of approaching search engine friendly (SEF) URLs in Joomla. Here, I explain these three methods of Joomla SEO and their pros and cons.
Search engine friendly URLs are very important if you want to achieve good positions in Google and other search engines. Firstly, the URLs are a lot easier to understand for the user (more likely to be clicked). Secondly, and most importantly, they will (if well-built) contain keywords that the search engine may use in the indexation of the page and thus improve your rankings for those words.
The SEF of no-SEF
Joomla comes with a built-in SEO function, but it's not activated by default. Thus, you'll get long, non-optimized URLs that mean little or nothing to both visitors and search engines. They will most likely not help you getting better rankings in the search engines. Most websites that use these kinds of URLs are either built by someone who has no knowledge of SEO, or are to be used as intranet solutions etc.
http://www.mydomain.com/index.php?option=com_content&view=article&id=5535:article-title&catid=10027:category&Itemid=56
Joomla built-in SEF
The built-in SEF solution in Joomla is quite nice, and gives you an easy way to implement semi optimized URLs on your site. If you're using mod_rewrite (must be activated on the server) and .htaccess file, you will get URLs like this:
http://www.mydomain.com/index.php/the-section/the-category/5535-article-title-goes-here
Third-party SEF extension
The best solution if you really need control over your URLs is to install a third-party component like sh404SEF or ArtioSEF. I like sh404SEF best and have never used anything else in a production site.
If you use a third-party extension for SEF URLs, you will get URLs like this:
http://www.mydomain.com/the-section/the-category/article-title-with-keywords/
This is how I do it here on Joomlablogger.net and it's by far the best method if you want rankings in the search engines, or more specifically, in Google.
If you want to know more, you can read my tutorial on how to set up sh404SEF.
Download sh404SEF and other SEF-extensions for Joomla here
Good luck with your Joomla SEO efforts!