How to write an integration test in NUnit?

Yes, generally speaking, this is how to write a unit test/integration test. You observe some important guidelines:

• Distinct Act-Arrange-Assert steps
• The test name describes these steps (maybe it should have something like "ShouldSendOneOrder" at the end, "Should" is commonly used to describe the Assert).
• One Assert per test.

I assume you also obey other guidelines:

• Tests are independent: they don't change persistent state, so they don't influence other tests.
• Test realistic use cases: don't arrange constellations that violate business logic, don't do impossible acts. Or: mimic the real application.

However, I also see things that raise eyebrows.

• It's not clear which act you test. I think some "acts" belong to the arrange step.

• A method like producer.OrderOverview() makes me suspect that domain objects execute database interaction. If so, this would violate persistence ignorance. I think there should be a service that presents this method (but see below).

• It's not clear why dataGridView.DataSource = producer.OrderOverview(); is necessary for the test. If it is, this only aggravates the most serious point:

• Business logic and UI are entangled!!

  • Method like guest.SendOrderOverview() and producer.OrderOverview() are smelly: why should a domain object know how to present its content? That's something a presenter (MVP) or a controller (MVC) or a view model (MVVM) should be responsible for.
  • A method like guest.SendOrder(dataGridView) is evil. It ties the domain layer to the UI framework. This fixed dependency is evil enough, but of course you also need values from the grid view inside this method. So the business logic needs intimate knowledge of some UI component. This violates the tell - don't ask principle. guest.SendOrder should have simple parameters that tell it how to do its task and the domain shouldn't have any reference to any UI framework.

You really should address the latter point. Make it your goal to run this test without any interaction with DGV.

If you continue to bound sql in class,your test is not a big problem.

You can use this method when the program logic is very simple,But I suggest you study The Repository Pattern,as the logic becomes more complex.