I want to update my old XOOPS 2.3.3b website to the latest 2.5.1a version.
How and what's the safest way to do this?

1) Make a backup of your XOOPS directory and your database
2) Follow the directions on page 33 of the XOOPS Installation Guide

Also, you MAY want to try updating to 2.4.5 before you upgrade all the way to 2.5.1a. 2.5.1a still has some lingering bugs that need to be ironed out and might be very frustrating. If you upgrade to 2.4.5 and make sure your modules work you will be far ahead.. Then you can try them with 2.5.1a and if they don't work it is likely due to a bug or two still in 2.5.1a. Think 2.5.1a is close but might not be quite there yet.

Rodney