Backup everything — entire web root folders and the SQL database. Check the backups work. It never hurts to keep a backup of the backup somewhere, perhaps on another computer. The idea being is that if you have to delete everything and start out from scratch, you know you’ll be able to get back to where you are now.
You will have to re-build your theme, as the BuddyPress theme structure changed since the version you are using. You’ll probably be able to keep your WordPress theme, but you’ll essentially have to build a new BuddyPress theme, or be happy with using the (new) default BuddyPress theme. You can check out the default theme on http://testbp.org/.
I would suggest you get your theme sorted out before you upgrade.
It’d be massively easier starting from scratch with a new BuddyPress installation, but I’m assuming you can’t do that. The upgrade process from this old versions will be complex. Definitely do it in steps, don’t jump to the latest version.
0) Disable BuddyPress and all other plugins. Revert to standard WP theme. Get WPMU upgraded to 2.9.2.
1) Get BuddyPress updated to 1.1.3.
2) Get new theme ready (or use BP-Default) and then upgrade to BuddyPress 1.2.4
3) Upgrade WPMU to WP 3.1.1 (latest version)
4) Upgrade BP to 1.2.8 (latest version)
You’ll need to test this upgrade process / order of events before you have a go on your live site. Set up a local test site, or on a test server, and try this there. I haven’t done any upgrades like this (keeping the data from an old version), but good luck
I’ll clarify when I say “upgrade BuddyPress”, I mean update the files and reactivate the plugin, then visit the plugins page in wp-admin. Then before the next step, deactivate BuddyPress. You won’t need to toggle between the BP Default theme during this.