First Shape: all four legs landing roughly perpendicular to the ground, which is usually the first steps a horse attempts. It can be useful for working transitions within gait, but keeping the horse from hollowing in a "square" piaffe is difficult, as is attaining animation.
Third Shape: on the forehand, generally with the front legs coming slightly behind the vertical but the hind legs landing under the hip. This is usually a result of over-reliance on the whip and/or use of pillars. Often very flashy movement behind, very little in front. Often disunited and/or laterally uneven.
Fourth Shape: Front legs land roughly perpendicular to the ground, hind legs somewhat under. This is the shape that can be developed into the levade or pesade, and from there into other airs. The pelvis is tipped, haunches lowered, and weight clearly on the haunches. Often the hind of each diagonal will land a hair before the fore, but they should pick up together. Common flaw: a cowhocked, wide behind way of sitting; this is not immediately problematic, but something to be wary of. If it is extreme in an otherwise straight horse, it may indicate a lack of strength or conditioning.