What you want to do in a unit test is make sure that the method does the job that it is supposed to do. If the method uses dependencies to accomplish it's work, you would mock those dependencies out and make sure that your method calls the methods on the objects it depends on with the appropriate arguments. This way you test your code in isolation.
One of the benefits to this is that it will drive the design of your code in a better direction. In order to use mocking, for example, you naturally gravitate towards more decoupled code using dependency injection. This gives you the ability to easily substitute your mock objects for the actual objects that your class depends on. You also end up implementing interfaces, which are more naturally mocked. Both of these things are good design patterns and will improve your code.
In order to test your particular example, for instance, you might have your class depend on a factory to create connections to the database and a builder to construct parameterized SQL commands that are executed via the connection. You'd pass these mocked versions of these objects to your class and ensure that the correct methods to set up the connection and command, build the correct command, execute it, and tear down the connection were invoked. Or perhaps, you inject an already open connection and simply build the command and invoke it. The point is your class is built against an interface or set of interfaces and you use mocking to supply objects that implement those interfaces and can record invocations and supply correct return values to the methods that you expect to use from the interface(s).