First, make sure that your Joomla 1.7 application is updated to the latest version of the 1.7 branch - Joomla 1.7.4. Then, go to Extensions -> Extensions Manager page in your Joomla administrative area.
On this page you have to locate the Update tab and click on it. It will take you to the page, responsible for the update process.
Once you are on this page, press the "Find Updates" button in the upper menu. It will check for the latest Joomla upgrade available.
In few seconds the new Joomla version should appear. Select it and press the "Update" button. It will download the appropriate upgrade package and apply it to your site.
In few seconds the update process will complete and you will have a working Joomla 2.5 ready to be used! Since the new version of Joomla uses the same template engine, your website front end should not be changed in any way.
