Baseline your Database and call this Version 0.1.0
As you need to make changes to it, like add columns, data etc. Script this and add this to the source control of your choice. Call this file something like:
Version-0.1.1.sql
As you make more and more changes the amounts of files will be added to.
Version-0.1.2.sql
Version-0.1.3.sql
Version-0.1.4.sql
Of course you will test these before you deploy to live. As you are working with what is a legacy system I would probably shy away from investment in expensive tools for what is a legacy system in the first place.
To bring a database to a particular version you would run the scripts in the order. Obviously in each script you have failover etc that handles anything that may go wrong within the scripts.
It is a manual process but the best points are it's cheap, easily to understand, does not require much expense and it's a methodical system to manage change.
Note: Obviously deploy scripts to a UAT version before directly on Live.