How is the rank of a Sergeant army person indicated?

It varies between uniforms. On the formal uniforms (Class A, Dress Blues), the rank insignia (three chevrons pointing upwards) is worn mid-sleeve on either side. If the trench coat is worn with this uniform, then metallic pin-on rank insignia is worn on the collar points.

On the Class B uniform (dress uniform with either short sleeve button up shirt or long sleeve button up shirt), the rank insignia is sewn into black shoulder boards which are worn on the epaulets.

On the phased out Battle Dress Uniform (BDUs) and Desert Combat Uniform (DCUs), the rank insignia was worn on the collar points, and could either be sewn on fabric insignia, or pin-on fabric insignia.

On the Army Combat Uniform (which replaced the BDUs and DCUs), the rank insignia is fabric - black chevrons sewn onto an olive background. This is velcro backed, and is affixed to a velcro tab on the front of the ACU top.

Enlisted personnel do not wear rank on the beret, but, on the patrol cap and kevlar helmet, it is worn on the front, either in sewn on fabric form, or pin on metallic form.