These are the steps to run an upgrade from CUCM6 to CUCM7 via the web interface.
First you have to go on the Cisco Unified OS Administration web interface.
You have to log yourself with the proper credentials (usually you have the account ccmadministrator for the CUCM Administration and the account admin for the OS Administration, this would be the same account for SSH access), it will depend on your installation.
Once i am logged, you can see that the actual version is 6.1.2.1000-13
You then have to click on Software Upgrades > Install/Upgrade
At this point you can insert the CUCM 7 DVD on your server.
Indicate / as Directory, leave the other fields empty, and click Next
The CUCM7 version should be detected, click Next
I choose to not reboot directly after the installation, (default choice) and I click Next
Now the upgrade is running, go take a coffee (this is a mandatory step).
If you close this page by mistake, you can open an another one and return on it, this won’t affect the upgrade, which is running locally on the server.
You would get this page (when you navigate to Software Upgrades > Install Upgrades) and would have to click on Assume Control.
And you get the previous page with the logs running.
On your CUCM you have 2 partitions, the active one and the inactive one. For now the version number 6 is the active one, once the upgrade will be done, the version 7 will be on the inactive one. So we will basically just Switch version.
This is usefull if you notice a problem after the upgrade to go back quickly on the previous version.
After one hour of upgrade, this is done !
We navigate to the Partition Versions. Show > Software
We can see the 2 versions
We are now going to Switch versions.
Navigate to Settings > Version
Just click Switch Version 
You have a notification, just click OK !
Now the Switching process is running.
Now go take another coffee…
The server will reboot and do its stuff :-)
After the Switch (random time, it took 10minutes here) , go back to the web administration page.
Go back on Show > Software (Still on the OS Administration section).
The Active version is the 7.0.1.11000-2 !
Congratz.
