When logging into a sandbox for the first time, DemandTools will provide an option to link the sandbox directly to the existing production organization simply by typing in the production organization ID in the space provided. DemandTools will then AUTOMATICALLY look up the production org in our authentication servers and update the sandbox expiration date to match.
The Salesforce Organization ID can be found by logging into the production account in the Salesforce User Interface then Setup -> Administration Setup -> Company Profile -> Company Information. The field, "Salesforce.com Organization ID", is in the right-hand column and will start with 00D.