That's quite an undertaking.
Make sure you have good backups and that the host running that WordPress installation has the minimum PHP and mysql requirements for the current version.
You'll need to upgrade in stages, switch to the default theme and deactivate all of the plugins.
2.3.3 -> 2.5.1 -> 2.6.5 -> 2.7.1 -> 2.8 -> 2.8.6 -> 2.9.2 -> 3.0.6 -> 3.1 -> 3.2 -> 3.3.1
You get the idea. I believe you may be able skip one or two of those versions but I'm not 100% sure of that.
Also, as you are probably aware the admin GUI has changed dramatically since 2.3.3 so make sure/prepare whoever is using that blog doesn't get massive culture shock.