I do not find good documentation on what scenarios we should run the tests and also how to deploy them.
You create SQL Server unit tests to help identify code defects that might cause incorrect application behavior. For instance, you can create a SQL Server unit test that verifies the behavior of several stored procedures.
First create a SQL server Unit test then use visual studio to run the tests
There are few examples and step by step on how that can be achieved Walkthrough: Creating and Running a SQL Server Unit Test
Then How to: Run SQL Server Unit Tests using Visual studio 2010 and 2012. I am not sure if others version will work.
I can repo this from my end and let you know
Regards,
Oury