From the Download page...

"The regular upgrade procedure works for upgrading from any version of b2evolution to any more recent version. b2evolution's installer/upgrader will automatically detect which older version you are upgrading from."
http://b2evolution.net/downloads/index.html

1. Back up all your current files & your database
2. Upload all the new files and simply run the upgrader thats supplied.
3. Remember to edit the _basic_config.php file with your password etc

Thank you

The upgrade path starts with making a backup of the 0.9.x database.
If you get stuck contact me, I'm the expert on ruined databases.

Good luck