Mockito offers a one-size-fits-all mehtod to create mocks of (non-final) classes and interfaces.

Dependency mock = Mockito.mock(Dependency.class);

This creates a mock instance of Dependency regardless of whether Dependency is a interface or class.

It is then possible to stub method calls to that mock using the Mockito.when(x).thenReturn(y) notation.

Mockito.when(mock.possiblyBuggyMethod()).thenReturn("someString");

So that calls to Dependency.possiblyBuggyMethod() simply return "someString".

There is another notation that is discouraged in most use cases as it is not typesafe.

Mockito.doReturn("someString").when(mock).possiblyBuggyMethod()

While a simple mock returns null (or defaults for primitives) to every call, it is possible to change that behaviour.

Dependency mock = Mockito.mock(Dependency.class, new Answer() {

        @Override
        public Object answer(InvocationOnMock invocationOnMock) throws Throwable {
            return "someString";
        }
    });

or using lambdas:

Dependency mock = Mockito.mock(Dependency.class, (Answer) invocationOnMock -> "someString");

This examples return "someString" to every invocation but it is possible to define any logic in the answer-method.

Class under test:

public class GreetingsService { // class to be tested in isolation
    private UserService userService;

    public GreetingsService(UserService userService) {
        this.userService = userService;
    }

    public String getGreetings(int userId, LocalTime time) { // the method under test
        StringBuilder greetings = new StringBuilder();
        String timeOfDay = getTimeOfDay(time.getHour());
        greetings.append("Good ").append(timeOfDay).append(", ");
        greetings.append(userService.getFirstName(userId)) // this call will be mocked
                .append(" ")
                .append(userService.getLastName(userId)) // this call will be mocked
                .append("!");
        return greetings.toString();
    }

    private String getTimeOfDay(int hour) { // private method doesn't need to be unit tested
        if (hour >= 0 && hour < 12)
            return "Morning";
        else if (hour >= 12 && hour < 16)
            return "Afternoon";
        else if (hour >= 16 && hour < 21)
            return "Evening";
        else if (hour >= 21 && hour < 24)
            return "Night";
        else
            return null;
    }
}

Behavior of this interface will be mocked:

public interface UserService {
    String getFirstName(int userId);

    String getLastName(int userId);
}

Assume actual implementation of the UserService:

public class UserServiceImpl implements UserService {
    @Override
    public String getFirstName(int userId) {
        String firstName = "";
        // some logic to get user's first name goes here
        // this could be anything like a call to another service,
        // a database query, or a web service call
        return firstName;
    }

    @Override
    public String getLastName(int userId) {
        String lastName = "";
        // some logic to get user's last name goes here
        // this could be anything like a call to another service,
        // a database query, or a web service call
        return lastName;
    }
}

Junit test with Mockito:

public class GreetingsServiceTest {
    @Mock
    private UserServiceImpl userService; // this class will be mocked
    @InjectMocks
    private GreetingsService greetingsService = new GreetingsService(userService);

    @Before
    public void setUp() {
        MockitoAnnotations.initMocks(this);
    }

    @Test
    public void testGetGreetings_morning() throws Exception {
        // specify mocked behavior
        when(userService.getFirstName(99)).thenReturn("John");
        when(userService.getLastName(99)).thenReturn("Doe");
        // invoke method under test
        String greetings = greetingsService.getGreetings(99, LocalTime.of(0, 45));
        Assert.assertEquals("Failed to get greetings!", "Good Morning, John Doe!", greetings);
    }

    @Test
    public void testGetGreetings_afternoon() throws Exception {
        // specify mocked behavior
        when(userService.getFirstName(11)).thenReturn("Jane");
        when(userService.getLastName(11)).thenReturn("Doe");
        // invoke method under test
        String greetings = greetingsService.getGreetings(11, LocalTime.of(13, 15));
        Assert.assertEquals("Failed to get greetings!", "Good Afternoon, Jane Doe!", greetings);
    }
}

@Spy annotation (or method) can be used to partially mock an object. This is useful when you want to partially mock behavior of a class. E.g. Assume that you have a class that uses two different services and and you want to mock only one of them and use the actual implementation of the other service.

Side Note: Although philosophically I wouldn't consider this a "pure unit test" in a true sense, as you are integrating a real class and not testing your class under test in complete isolation. Nevertheless, this could be actually useful in the real world and I often use it when I mock the database using some in memory database implementation so that I can use real DAOs.

Class under test:
public class GreetingsService { // class to be tested in isolation
    private UserService userService;
    private AppService appService;

    public GreetingsService(UserService userService, AppService appService) {
        this.userService = userService;
        this.appService = appService;
    }

    public String getGreetings(int userId, LocalTime time) { // the method under test
        StringBuilder greetings = new StringBuilder();
        String timeOfDay = getTimeOfDay(time.getHour());
        greetings.append("Good ").append(timeOfDay).append(", ");
        greetings.append(userService.getFirstName(userId)) // this call will be mocked
                .append(" ")
                .append(userService.getLastName(userId)) // this call will be mocked
                .append("!");
        greetings.append(" Welcome to ")
                .append(appService.getAppName()) // actual method call will be made
                .append(".");
        return greetings.toString();
    }

    private String getTimeOfDay(int hour) { // private method doesn't need to be unit tested
        if (hour >= 0 && hour < 12)
            return "Morning";
        else if (hour >= 12 && hour < 16)
            return "Afternoon";
        else if (hour >= 16 && hour < 21)
            return "Evening";
        else if (hour >= 21 && hour < 24)
            return "Night";
        else
            return null;
    }
}

Behavior of this interface will be mocked:

public interface UserService {
    String getFirstName(int userId);

    String getLastName(int userId);
}

Assume actual implementation of the UserService:

public class UserServiceImpl implements UserService {
    @Override
    public String getFirstName(int userId) {
        String firstName = "";
        // some logic to get user's first name
        // this could be anything like a call to another service,
        // a database query, or a web service call
        return firstName;
    }

    @Override
    public String getLastName(int userId) {
        String lastName = "";
        // some logic to get user's last name
        // this could be anything like a call to another service,
        // a database query, or a web service call
        return lastName;
    }
}

Behavior of this interface won't be mocked:

public interface AppService {
    String getAppName();
}

Assume actual implementation of AppService:

public class AppServiceImpl implements AppService {
    @Override
    public String getAppName() {
        // assume you are reading this from properties file
        String appName = "The Amazing Application";
        return appName;
    }
}

Junit test with Mockito:

public class GreetingsServiceTest {
    @Mock
    private UserServiceImpl userService; // this class will be mocked
    @Spy
    private AppServiceImpl appService; // this class WON'T be mocked
    @InjectMocks
    private GreetingsService greetingsService = new GreetingsService(userService, appService);

    @Before
    public void setUp() {
        MockitoAnnotations.initMocks(this);
    }

    @Test
    public void testGetGreetings_morning() throws Exception {
        // specify mocked behavior
        when(userService.getFirstName(99)).thenReturn("John");
        when(userService.getLastName(99)).thenReturn("Doe");
        // invoke method under test
        String greetings = greetingsService.getGreetings(99, LocalTime.of(0, 45));
        Assert.assertEquals("Failed to get greetings!", "Good Morning, John Doe! Welcome to The Amazing Application.", greetings);
    }

    @Test
    public void testGetGreetings_afternoon() throws Exception {
        // specify mocked behavior
        when(userService.getFirstName(11)).thenReturn("Jane");
        when(userService.getLastName(11)).thenReturn("Doe");
        // invoke method under test
        String greetings = greetingsService.getGreetings(11, LocalTime.of(13, 15));
        Assert.assertEquals("Failed to get greetings!", "Good Afternoon, Jane Doe! Welcome to The Amazing Application.", greetings);
    }
}

In your class that is under test, you may have some private fields that are not accessible even through constructor. In such cases you can use reflection to set such properties. This is a snippet from such JUnit test.

@InjectMocks
private GreetingsService greetingsService = new GreetingsService(); // mocking this class

@Before
public void setUp() {
    MockitoAnnotations.initMocks(this);
    String someName = "Some Name";
    ReflectionTestUtils.setField(greetingsService, // inject into this object
        "name", // assign to this field
        someName); // object to be injected
}

I'm using Sptring's ReflectionTestUtils.setField(Object targetObject, String name, Object value) method here to simplify, but you can use plain old Java Reflection to do the same.