right out of the docs that were included in the download:

Upgrading from a previous version of b2evolution
Before you begin, please note that some network features of b2evolution require you to agree our simple Terms of service.

Backup all your b2evolution files. Take special care of the files you may have modified, including /conf, skins, blog templates, stubfiles, etc...
You should also backup your database if you can. This functionality should be provided by your host.
Delete all your existing b2evolution files from your site before uploading the new ones! This will ensure you don't keep unnecessary files on your server after upgrading. It's also better for security.
Upload all new b2evolution files from the /blogs folder to your site. We cannot stress this enough: ALL FILES! And that means you can't reuse your customized files, including /conf, skins, blog templates, stubfiles, etc. as they are!

That means you will have to customize all these files again. We're sorry but, due to the pace of development and adding of new features, we cannot guarantee that anything will work if you keep older files in place. However, since you have backed up all these files in step 1, you can try to partially reuse them once the upgrade process is done. See step 8 below.
Run the installation script on your server. It is located in http://yoursite.com/yourblogsfolder/install . Then, simply follow the on screen instructions.

The installer will ask you basic configuration settings (unless you have already updated /conf/_config.php before uploading), then allow you to run a database upgrade from any b2evolution version to the new one.
Check to make sure the new installation works.
On production servers, it is recommended that you delete the /install subfolder.
It's now time to bring back your previous customizations. We recommend you get yourself a diff/merge tool like WinMerge. This will allow you to easily compare your old (backuped) files with the new files (even whole directories at once) and report changes accordingly.

You can also check the manual or the forums for notes on upgrading specific files from a specific version to another.
After basic install is done, there are a few tricky things you may need to take care of (online manual).