Upgrading nowadays is fairly easy and fast with the Plugin system.
Before you go you must remember whether or not you made any file modifications (or your other admins), for which hack and possibly where, as you'll have to redo those changes.
Depending on the size of your database you can either make a backup via the vBulletin admincp, phpMyAdmin or SSL I believe (or SSH, can't remember). Simply google "MySQL database backup" and you'll find the info you need.
An ftp backup is simple, simply copy-paste your forum dir to any folder on your computer and it'll download it to your pc.
I'd also recommend looking for any Products/Plugins you have installer (look them up here or at vb.org), and check whether they have a newer version out, and whether or not the current version works with vB 3.5.4
I'd also recommend you putting a new index.html file in the forum dir, saying the board is temp. unavailable.
Once you've done all that you can simply download the latest version from the vB members' area (pick the No Images Pack), unzip it and upload the Upload dir to your FTP (make sure the skeletions match, i.e. showthread.php overwrites showthread.php).
After this run
the upgrade script, renable your forums and you're done ;).
Also, the
vBulletin Manual has some good information about upgrading. Simply enter "upgrade" in the search field.
Lastly, if you have a heavily modded forum and this is your first time, you might want to test it out on a testboard first (instructions on how to run a local test board can be found
here and
here). You could also run an online copy of your board, which is quite a lot easier.
Hope this helps! ;)