It's actually pretty simple, just takes time.
You probably need to renew your member area access/download privileges, but when you do you'll have access to ubb.classic 6.7.3 - follow the upgrade instructions and in a couple hours you'll be running the most recent version of your software.
After that it will take a few more hours to install ubb.threads and import everything (except styles) into it.
That's it in a very small nutshell, but it's doable. If you'd rather someone do it for you, open a support ticket here or I am available for reasonable rates
