Since 2.5 is the current LTS version until 3.5; the majority of the core changes are deprecated versus being completely removed. Meaning you can still use them and there are overall not many things required to migrate a 2.5 component, for now. I would definitely read through the walk through provided by Soren, but here are the three "major" required changes to get a 2.5 component working on 3.1 and above Joomla... with caveats of course! :D
1) Make sure all your view classes extend JViewLegacy
2) Make sure your primary controller extends JControllerLegacy instead of JController
3) Make sure your primary component entry point (my_component_name.php file in component root) use JControllerLegacy::getInstance('my_component_name') instead of JController::getInstance('my_component_name')