When you install Office 2010, you need to have a valid key to use it after the trial period. In case you have activated it with a valid key and at a later point of time, if you want to change the product keys, Office 2010 does not provide a direct interface to change it. To change the product keys, you need to run the installer and you can do it in 2 ways. Both of them actually involve the same method, but different ways to arrive at it.
If you have the full installer of Office 2010, either the downloaded version or the DVD version, run the installer.
Once the set up loads the necessary file, it shows you options to change the product key.
Click continue and in the next step, enter the new product key.
Click Continue and your new key would be validated online.