How do I calculate someone's age in Java?

Check out Joda, which simplifies date/time calculations (Joda is also the basis of the new standard Java date/time apis, so you'll be learning a soon-to-be-standard API).

EDIT: Java 8 has something very similar and is worth checking out.

e.g.

LocalDate birthdate = new LocalDate (1970, 1, 20);
LocalDate now = new LocalDate();
Years age = Years.yearsBetween(birthdate, now);

which is as simple as you could want. The pre-Java 8 stuff is (as you've identified) somewhat unintuitive.

JDK 8 makes this easy and elegant:

public class AgeCalculator {

    public static int calculateAge(LocalDate birthDate, LocalDate currentDate) {
        if ((birthDate != null) && (currentDate != null)) {
            return Period.between(birthDate, currentDate).getYears();
        } else {
            return 0;
        }
    }
}

A JUnit test to demonstrate its use:

public class AgeCalculatorTest {

    @Test
    public void testCalculateAge_Success() {
        // setup
        LocalDate birthDate = LocalDate.of(1961, 5, 17);
        // exercise
        int actual = AgeCalculator.calculateAge(birthDate, LocalDate.of(2016, 7, 12));
        // assert
        Assert.assertEquals(55, actual);
    }
}

Everyone should be using JDK 8 by now. All earlier versions have passed the end of their support lives.

Calendar now = Calendar.getInstance();
Calendar dob = Calendar.getInstance();
dob.setTime(...);
if (dob.after(now)) {
  throw new IllegalArgumentException("Can't be born in the future");
}
int year1 = now.get(Calendar.YEAR);
int year2 = dob.get(Calendar.YEAR);
int age = year1 - year2;
int month1 = now.get(Calendar.MONTH);
int month2 = dob.get(Calendar.MONTH);
if (month2 > month1) {
  age--;
} else if (month1 == month2) {
  int day1 = now.get(Calendar.DAY_OF_MONTH);
  int day2 = dob.get(Calendar.DAY_OF_MONTH);
  if (day2 > day1) {
    age--;
  }
}
// age is now correct