-    Go to the administrative end of your Joomla website -> Global Configuration and make sure that both Search Engine Friendly URLs and Use Apache mod_rewrite are set to Yes.
-    Make sure you have renamed the htaccess.txt file in your Joomla folder to .htaccess.
If you follow all of the steps above you should have a fully operational Joomla website with the SEF functionality enabled. For testing purposes you can temporarily disable the Search Engine Friendly URLs in order to check whether they are the cause for your issues.