How to use the annotated @TestSetup method in Tests?

Yes, you must re-query the data. Sometimes you might use constant strings to pull in, for instance a custom setting:

static final String SETTING_NAME = 'foo';

@TestSetup
static void setup()
{
    insert new MySetting__c(Name=SETTING_NAME);
}

static testMethod void testBar()
{
    MySetting__c relevantSetting = MySetting__c.getInstance('foo');
}

Often, this approach is used for configuration data that will be common to your tests, be it in a Custom Object or Custom Setting.

Similar to your use case, it's a nice convenience when testing an extension.

@TestSetup
static void setup()
{
    insert new Case(/*data*/);
}
static StandardController getController()
{
    return new ApexPages.StandardController([SELECT ... FROM Case LIMIT 1]);
}

static testMethod void testMyExtension_Constructor()
{
    ApexPages.StandardController controller = getController();

    Test.startTest();
        MyExtension extension = new MyExtension(controller);
    Test.stopTest();

    // assert on behavior
}
static testMethod void testSomeMethod()
{
    MyExtension extension = new MyExtension(getController());

    Test.startTest();
        extension.someMethod();
    Test.stopTest();

    // assert on behavior
}

It is a correct way. I would, however, like to identify few benefits of @testSetup below

1. Use this annotation if you want to create test data once and use it in all test methods of your class. Therefore, you don't need to recreate the data again.
2. Records created in a test setup method are rolled back at the end of test class execution.
3. @testSetup methods are executed first in the class before any test methods. You may have multiple @testSetup methods in your class, however, their execution order is not guaranteed.

See also:

Test Setup Method Considerations

Test setup methods are supported only with the default data isolation mode for a test class. If the test class or a test method has access to organization data by using the @isTest(SeeAllData=true) annotation, test setup methods aren’t supported in this class.

• Multiple test setup methods are allowed in a test class, but the order in which they’re executed by the testing framework isn’t guaranteed.
• You can have only one test setup method per test class.
• If a fatal error occurs during the execution of a test setup method, such as an exception that’s caused by a DML operation or an assertion failure, the entire test class fails, and no further test methods are executed.
• If a test setup method calls a non-test method of another class, no code coverage is calculated for the non-test method.