Sometimes you can easily spot a number that will divide evenly into both the numerator and the denominator. (By carrying out this division you will reduce the fraction to a lower form.)
You then check if you can spot another common denominator, for this "reduced fraction", and if so, then divide the numerator and denominator again to further reduce the fraction. When the only common divisor is 1, you have reduced the fraction to its lowest form.
(If you cannot spot an obvious divisor try 2 or 3 to begin with.)