This guide works for Jommla 3.2.x as well as 3.3.x

If you are thinking to migrate it to 3.x.x version from your present 2.5.x version, this guide is for you. Though 2.5.x is Long Term Support Release, so it is not required to migrate (or upgrade) to newer version, still if you can't wait for 3.5 version you must be thinking to migrate it.

First of all, update your present website to latest Joomla 2.5.x version.

Follow these steps carefully:

Step #1: Backing up

Back-up your complete website (database and files). This is very important unless you are running test operations. Even after following this guide, errors are likely when you try migrating. The process involves fixing those errors and then trying again. So you need to restore your website, and again try to migrate.

Duplicating Database: If you have cPanel access, go to phpMyAdmin and create a copy of database.

Add DB user to this new database as well.

Duplicating Files: Create a new folder (say joomla), and copy all your Joomla files to this new folder.

We have dulicated database and files, now we are first going to test migration with duplicated files and databse. Your main site is safe and running.

From step 2, you are going to work with duplicated files.

Step #2: Preparation

Check out for extensions and template you are using for availability in Joomla 3.x version. In case they are not available, find an alternative or check if development is in progress.

Update your database. Go to Extension Manager --> Database, and fix any errors.

Uninstall any outdated extensions (especially plugins and extensions) you may have installed and not using them. The time is for fresh and updated website.

Step #3: STS Support

Go to Components --> Joomla Update --> Options. Change update server to Short Term Support. Save and Close.

Step #4: Migrate

Click on Install the update. If you are not able to find this option immediately, then go to Extensions --> Extension Manager --> Update --> Purge Cache.

Step #5

If installed successfully, enjoy your new Joomla version or else restore backup created in the first step. Check configuration, menu systems, modules, linking structure, etc. to ensure that the new website is similar to the old one.

Fixing Errors - 3rd Party Extensions

Most of the errors occur when you hit the update button (in step 4), the automatic updater works well for a few seconds and then your website breaks with some error or blank screen.

Why This Happens?

Joomla automatic updater works with Joomla core files only. Most of the times, third party extensions (especially components and plugins) cause problems.

So propably the best way is to uninstall problematic extensions (other than by Joomla Project), then migrate and re-install newer versions of extensions.

What About Data in Extensions?

Modules and plugins do not have any data; you may just need to reconfigure them. For extensions that have content, most of time these are stored in database tables which will not be lost while un-installing. When you re-install after migrating data will be automatically restored. Some extensions have their own back-up and upgrade features. You need to check with them.

Fixing Errors - Remember Me Plugin

If you get errors in following file:

plugins/system/remember/remember.php on line

Rename the file to rememberBAK.php, and then try again.

Blank Screen Problem 

You cannot solve any issue unless you know it. By default, Joomla had lower level of error reporting. You can change that in configuration file. Edit your configuration.php file: 

public $error_reporting = 'default';

To

public $error_reporting = 'maximum';