Graduated Long Layers
With this style, Lily Adridge's signature look, the first layer should start around the chin area to offset the look of a strong jawline. It's also a good idea to have all of the layers turning inward, not outward, so that it narrows the face a bit.
A Sheared, Short Tapered Cut
What makes a style like Miley's okay for a square face is the extra height on top. It creates the illusion of a longer face, causing the square to appear more rectangular in shape.
The Lob
When you look at the long bob (aka lob) from the front, like Olivia Wilde's, the two straight side panels of hair that hang down right beside each cheekbone, slightly mask the width of the cheekbones, forehead, and jawline that widen a square face. These factors combined is why this style is spot-on for an angular shape.
An Off-Center Part
A slightly off-center part (somewhere between a side and middle part), like J. Hud is flaunting here, helps to round out a square face. It frames it just so, cutting out the width of your face and offsetting the angles.
Rounded Fringe
If you want bangs or have them already, you'll want to make sure that the outside corners of your fringe is an inch to an inch and a half longer than the center of the bangs. This creates the framing effect, drawing the attention inward, ultimately softening a wider face.
A Low Chignon
If you want to wear your hair back, go for a relaxed low chignon with a slightly off-center part, and pieces pulled out around the temple area. The combination of the above will counteract the squareness of your face, and the pieces framing it will also take away any width and distract from any harsh lines.
A Below the Collarbone Cut
This length, coupled with layers that turn inward, frames your face just right. The graduated layers also cut off the broadness of the jawline and wide cheekbones. Jessica Biel is also rocking the rounded bang look, which also complements her square face shape by narrowing it out a bit.
