Then it is safe to say that you are running under the "advanced" one-click install of WordPress because:
1) It is the only one that was available six months ago (the "easy" one-click version was only added to the Control Panel in February, 2008
2) The "Easy" version never requires any action on your part to be kept "updated" - DreamHost handles all that for you "automagically".
No, you just have to use the panel to tell the DreamHost one-click system to upgrade your existing "one-click" installation of version 2.2.3 to version 2.5.2, and it will proceed.
That said, you should be aware that you may have some issues, as you have gone so long "past" the normal upgrade point (you have skipped many upgrades available since 2.2.3!).
Your theme may, or may not, be compatible with WordPress 2.5.1, and many of the plugins you may be using may require updated versions to work, if they work at all.
Given this situation, I'd make sure I made a backup of the database before I tried this upgrade. That way, if things go wrong, you can always go back (DreamHost stores your "old" 2.2.3 WordPress files in a ".old" directory for this purpose).