How do I print out the value of this boolean? (Java)

System.out.println(isLeapYear);

should work just fine.

Incidentally, in

else if ((year % 4 == 0) && (year % 100 == 0))
    isLeapYear = false;

else if ((year % 4 == 0) && (year % 100 == 0) && (year % 400 == 0))
    isLeapYear = true;

the year % 400 part will never be reached because if (year % 4 == 0) && (year % 100 == 0) && (year % 400 == 0) is true, then (year % 4 == 0) && (year % 100 == 0) must have succeeded.

Maybe swap those two conditions or refactor them:

else if ((year % 4 == 0) && (year % 100 == 0))
    isLeapYear = (year % 400 == 0);