The whole process unfortunaly is not easy. There are many suggestions posted here and there that one should update/upgrade all extensions on 2.5 installation first and then perform in-place upgrade of joomla 2.5 to 3.x via Joomla Update component st to Short Term Support. It was not working in my case with a "white screen" as a result. Finally I concluded that smooth transition is not the case. Below is my own approach to the problem:
- create a backup of your website e.g with Akeeba Backup (excellent extension, still free)
- restore the website to your own LAMP, XAMPP, or whatever you like
- install the extension allowing you exporting and importing from and to your db (I used J2XML that you can get from here: http://www.eshiol.it)
- install Joomla 3.x in separate directory
- export articles and users from 2.5 to 3.x
- recreate your template and other extensions - this of course can be painful