You will need the Full Write Connections permission to perform this action.
A connection can be edited from two places: the main Connections listing in the left-hand menu, or the Involvement > Connections tab on the person's profile.
Open the Edit Connection Dialog
Open the connection record by clicking it from either location above. In the upper-right of the record, click the Actions button and select Edit connection.
A pop-up will appear where you can update the details of the connection. See How do I add a connection? for an explanation of each field.
Helpful Tip
The connection type cannot be changed after the record has been created. If you need to switch the type, delete the old connection and create a new one using the correct type.