If you site is live then you shouldn’t directly update that, although update in the recent version of wordpress is very easy and seemless but that wasn’t the case in 2.1 though.
Also here is the list of steps that I will recommend you to take:
- Make the list of all plugins.
- Make sure none of the plugin’s are responsible for site’s main functionality. (As kaiser said its okay if they are only presentational).
- There is 99% chance that your theme will break with or at least will complain of deprecated functions with wordpress 3.1, so you have two options, either switch to standard theme or check your site for errors from theme after each upgrade until you are at 3.1
- Install the WordPress 2.1 on test machine and clone your live site, not all the data but at least the functionality.
- Disable all the plugins responsible for main functionlaity that you noted in Step 2
- Upgrade to the next stable version of wordpress that was released after your current version.
- Enable the plugins one by one and check your test site.
- If there are errors see if you can fix them or disable the plugin. You might also see errors from your theme if you haven’t switched to standard theme, so try to fix them too.
- If you have upgraded to WordPress 3.1 then Congratulations else goto Step 5.
Hope this will be helpful to you and you will have easy upgrade to 3.1.