>>>Hi,
>>>
>>>How do you update a database structure (default keys, constraint, etc) installed on the customer site with the changes you have made to your copy of SQL Server database? That is, I understand that I have to create some script and send it to the customer and instruct them to run this script, correct? How do you create such a script? TIA.
>>
>>We're using RedGate SQLCompare.
>
>Is this a commercial product? If so, is there a way to do it without buying a tool for that?

Yes, it's a commercial produce. I recommend to review this thread Compare SQL Tools Thread #1419284 Message #1419284, I believe there are some free tools mentioned there as well.