How should I set up my integration tests to use a test database with Entity Framework?

Thanks so much to @Justin and @Petro for your answers, which have helped me immensely. The solution I have come up with is a combination of the techniques you suggested. The solution described below provides a new database for each run of the tests, and a separate transaction for each test.

I added a connection string for my test database in the App.config of my Test project:

  <connectionStrings>
    <add name ="TestDatabase"
     providerName="System.Data.SqlClient"
     connectionString="Data Source=(LocalDb)\v11.0;Database=TestDatabase;Integrated Security=True"/>
  </connectionStrings>

I created a base class for my integration tests, to provide setup and teardown. Setup instantiates the context, creates the DB if it doesn’t exist yet and starts a transaction. Teardown rolls back the transaction.

public class EntityFrameworkIntegrationTest
{
    protected MyDbContext DbContext;

    protected TransactionScope TransactionScope;

    [TestInitialize]
    public void TestSetup()
    {
        DbContext = new MyDbContext(TestInit.TestDatabaseName);
        DbContext.Database.CreateIfNotExists();
        TransactionScope = new TransactionScope(TransactionScopeOption.RequiresNew);
    }

    [TestCleanup]
    public void TestCleanup()
    {
        TransactionScope.Dispose();
    }
}

Finally, I have a class that takes care of deleting the database after all the tests have run:

[TestClass]
public static class TestInit
{
    // Maps to connection string in App.config
    public const string TestDatabaseName = "TestDatabase";

    [AssemblyCleanup]
    public static void AssemblyCleanup()
    {
        Database.Delete(TestDatabaseName);
    }
}

I should add that I found this blog post about Entity Framework useful for a deeper understanding of what Entity Framework is doing under the hood / by convention.