This tutorial will explain how to restore a Joomla 2.5 site if you accidentally upgrade to Joomla 3.x.x. It assumes that you've run out of options and don't have a backup from which to restore. Before attempting this tutorial, you might want to trouble shoot your current 3.x.x site as it might be easier to stay on 3.x.x, depending on what errors you're getting. Post in the Joomla forum if you're unsure at any point. Please note that this tutorial is not for beginners and that beginners should likely hire someone to do this for them.
Steps: 1) Backup your files and database.
2) Download Akeeba SiteDiff: https://www.akeebabackup.com/downloads/akeeba-sitediff.html
3) Download the latest Stable Update package (not the Stable Full Package) version of Joomla 2.5.x.
4) Download the Stable Update package (not the Stable Full Package) version of Joomla 3 version that you updated to.
5) Run Akeeba SiteDiff using the 2.5 package as the starting version and the 3.x.x package as the current version in Akeeba SiteDiff. Let it finish processing.
6) Select "Added" and save the list.
7) Delete all files that are listed one-by-one. Note, if you know what you're doing and can differentiate between folders that contain only core content vs folders that contain core content and third party content, you can take shortcuts by deleting the highest level folder that contains only core content. For example, instead of deleting all the Isis files that are listed, you can delete the isis folder (administrator/templates/isis/) thus saving you a lot of time.
Here's an example of restoring a 2.5.8 site after updating to 3.0.2...the following files/folders would need to be deleted: CONTRIBUTING.md administrator/templates/isis/ administrator/templates/hathor/ administrator/components/com_content/ administrator/components/com_finder/ administrator/components/com_config/ administrator/components/com_modules/ administrator/components/com_categories/ administrator/components/com_admin/ administrator/components/com_menus/ administrator/language/en-GB/en-GB.mod_stats_admin.ini administrator/language/en-GB/en-GB.mod_stats_admin.sys.ini administrator/language/en-GB/en-GB.tpl_isis.ini administrator/language/en-GB/en-GB.tpl_isis.sys.ini administrator/modules/mod_stats_admin/ cli/deletefiles.php components/com_content/ images/headers/ language/en-GB/en-GB.tpl_protostar.sys.ini language/en-GB/en-GB.tpl_protostar.ini language/en-GB/en-GB.tpl_beez3.sys.ini language/en-GB/en-GB.tpl_beez3.ini layouts/ libraries/ media/plg_quickicon_extensionupdate/ media/jui/ media/plg_quickicon_joomlaupdate/ media/mod_languages/ modules/mod_login/ modules/mod_menu/ phpunit.xml.dist templates/beez3/ templates/protostar/
8) Upload your 2.5.x package (that you downloaded in step 2) into your Joomla root folder and then unzip it.
9) Your site should now work. Finally, log into your administrator and then go to Extensions (top menu) >> Extension Manager (sub menu) >> Database (tab) >> you should see some errors saying your database structure does not match your Joomla version >> click the Fix button (top right).
10) Celebrate and "pay it forward" :)