Mocking a DAO in Mockito

I'm just getting into testing of code. I have done unit tests before but haven't really isolated them. So they were more like integration test (indirectly). I want to give Mockito a try and I have added it to my Intellij IDE. But I have no idea of how to actually implement mocking at all. There are examples on their website but I just can't wrap my head around the concept of mocking. I know that one uses mocking to isolate the unit testing to ensure that the errors are in the unit itself and not in a dependency.

I wrote the following:

@Test
public void testChangeMemberReturnsTrue() throws Exception {
    Member tempMem = new Member();
    tempMem.setMemberFirstName("Swagrid");
    tempMem.setMemberLastName("McLovin");
    tempMem.setMemberID("SM666");

    SQLDUMMY.saveMember(tempMem);               //Save member to dummy DB.

    Member checkMem = new Member();
    ArrayList<Member> memArr = SQLDUMMY.getAllMembers();
    for (Member m : memArr) {                   // Look through all saved members
        if (m.equals(tempMem)) {                // If match, save to checkMem
            checkMem = m;
        }
    }
    assertTrue(tempMem.equals(checkMem));            // Make sure they are really equal.

    String newfirstname = "Darius";
    String newlastname = "DunkMaster";
    assertTrue(memhandling.changeMember(tempMem, newfirstname, newlastname));

}

And here is the actual method:

public boolean changeMember(Member mem, String n1, String n2) {
    try {
        ArrayList<Member> memArr = SQLDUMMY.getAllMembers();
        for (Member m : memArr) {
            if (m.equals(mem)) {
                m.setMemberFirstName(n1);
                m.setMemberLastName(n2);
                m.setMemberID(ensureUniqueID(m, m.getMemberID())); //Just a method call to another method in the same class to ensure ID uniqueness.
                return true;
            }
            else {
                return false;
            }
        }
    }
    catch (Exception e) {
        System.out.println("Error4.");
    }
    return false;
}

I'd like to mock the SQLDUMMY (Which I created just to see if my tests would pass at all, which they do.) The SQLDUMMY class looks like this:

public class SQLDUMMY {

private static ArrayList<Member> memberList = new ArrayList<>();
private static ArrayList<Ship> shipList = new ArrayList<>();

public static ArrayList<Member> getAllMembers() {
    return memberList;
}

public static void saveMember(Member m) {
    memberList.add(m);
}

public static void deleteMember(Member memIn) {
    memberList.remove(memIn);
}


public static void saveShip(Ship newShip) {
    shipList.add(newShip);
}

public static ArrayList<Ship> getAllShips() {
    return shipList;
}

public static void deleteShip(Ship s) {
    shipList.remove(s);
}

}

It basically just consists of getters and add/remove for the ArrayLists that act as a contemporary DB storage.

Summary: How can I mock the SQLDUMMY class (DAO), so it is no longer a dependency for the Unit tests?