7
1) Make sure, you have at least PHP 5.3.7 installed, and that you have the current versions of the modules that you want to update (e.g. News, MyAlbum)
2) Do backup of all the files, as well as the DB
3a) copy files from XOOPS 2.5.7 /htdocs to your XOOPS installation
3b) in case, you have moved or renamed the /xoops_lib and /xoops_data folders, makes sure that the files from these folders in XOOPS 2.5.7 go to the appropriate folders in your installation
4) copy the /upgrade folder to your XOOPS installation
5) go to
http://yoursite.com/upgrade and run it, this will include updating the System module
6) Update the PM, Profile, and Protector modules
7) Try to update your other modules and see if they work.
Before you make it all, you might also install
WampServer on your PC, copy your current Website there, incl. the DB, and test the upgrade over there first.