1.Starting with the legs, checking for conformational faults and correctness.
2.Next judging point is the body, or trapezoid. Making sure the horse fits into three circles or splitting the horse into thirds. 1/3 for the butt and hip, a 1/3 for the barrel, and 1/3 for the shoulder. Once those are sized to be equal or unequal you can take into consideration the slope of the shoulder and from point of buttock to the hip. This is where the trapezoid comes in. The shoulder and hip line should have the same angle, and the line from hip to whither should be even across the top.
3.Next is the neck and head. Length of head should not exceed length of neck, and I like longer necks on a horse. After that you will check the quality of the head, for femininity or masculinity, depend on the sex of the horse. Stallions should have a larger jaw and a wider head. Mares will have a much finer, prettier head. Also be sure to check for thickness of throat latch, as that determines how well the horse can travel whilst collected. Size of nostrils for air intake, and size and positioning of eyes for sight. Less important is length of ear.
4. Last is quality and quantity of muscle. A well defined chest forming an upside down V when viewed from the front, large gaskins and forearms and a well muscled hind end.
1 and 2 can be interchanged on preference along with 3 and 4, depending on what the judge feels is most important. But 1 and 2 should always place a horse before 3 or 4 will. You need a conformationally correct horse over a "pretty" one, which 3 and 4 I consider to be the pretty options. When presented with 2 horses that are equal in 1 and 2, then 3 and 4 will place one above the other in a class.
If you would like more of an explanation, please ask!