The pertinent US Army Field Manual in force at the time (FM 21-75 Scouting, Patrolling, and Sniping) does mention the usage of spotters. The manual specifies two kinds of sniping;

Mobile Sniper:

The mobile sniper acts alone, moves about frequently, and covers a large, but not necessarily fixed area. He may be used to infiltrate enemy lines and seek out and destroy appropriate targets along enemy routes of supply and communication....Therefore, although the mobile sniper must be an expert shot at all ranges, he must be trained to stalk his target until he is close enough to insure [sic] that it will be eliminated with his first shot.

Stationary Observer-Snipers:

Teams of two snipers may work together, operating sniping posts assigned definite sectors of fire. Each sniper is equipped with field glasses. His rifle has telescopic sights. One man acts as an observer, designating the targets discovered by the firer and observing the results of the fire...Because this duty is tiring, it is necessary that the observer and the sniper exchange duties every 15 to 20 minutes.

During WWII, sniper training in the US Army was very decentralized; there was no "sniper school" or equivalent. Each rifle company was authorized three M1903A4 rifles, to be distributed one per rifle platoon at the discretion of the platoon leader. Those who would be designated as snipers were ostensibly the best shots in the company. The following proficiencies are recommended in the field manual;

• Advanced training in rifle marksmanship

• Elimination based on shot groups fired at 300 and 600 yards

• Additional practice in range estimation under all conditions of visibility

• Training in identifying and locating sounds to include those of weapons

• Training in selection of firing positions

• Training in observation and visual searching of areas under varying conditions of visibility

• Use of concealment and camouflage

• Firing at field targets at unknown distances with iron sights

• Nomenclature and care of telescopic sights

• Zeroing telescopic sight at 400 yards

• Study of trajectory, drift, effects of wind and light

• Known-distance firing with telescopic sight to determine hold-off [aiming low for targets under 400 yards, and high for targets over 400 yards]

• Firing at unknown ranges, using telescopic sight

• Fairly obvious targets

• Concealed targets

• Training in selection of and movement by concealed routes

• Final examination over terrain not previously used

Platoon Headquarters:

Quantity	SSN	Rank	Role
1c	1542	First or Second Lieutenant	Platoon leader
1r	745	Technical Sergeant	Platoon Sergeant
1gr	745	Staff Sergeant	Platoon guide
2r	745	Pvt./Pfc.	Messenger

Equipment:

Equipment	Quantity
Carbine, cal. .30, M1	1
Launcher, grenade, M7	1
Rifle, U.S., cal. .30, M1	4

Three Rifle Squads, each:

Quantity	SSN	Rank	Role
1r	745	Staff Sergeant	Squad leader
1gr	745	Sergeant	Squad leader, assistant
7r(2gr)	745	Pvt./Pfc.	Rifleman
1b	746	Pvt./Pfc.	Rifleman, automatic
1r	746	Pvt./Pfc.	Rifleman, automatic, assistant
1r	604	Pvt./Pfc.	Ammunition bearer

Equipment:

Equipment	Quantity
Launcher, grenade, M7	3
Rifle, Browning, automatic, cal. .30, M1918A2	1
Rifle, U.S., cal. .30, M1	11

Equipment for Issue:

Equipment	Quantity
Rifle, U.S. cal. .30, M1903A4 (sniper's)	1

b: armed with rifle, automatic, cal. .30

c: armed with carbine, cal. .30

g: armed with launcher, grenade, M7. Three individuals per rifle squad will be armed with launcher, grenade, M7

r: armed with rifle, U.S., cal. .30, M1. One individual per rifle platoon, as designated by rifle platoon leader, will be armed with rifle, cal. .30, M1903A4.

Sources:

FM 21-75 Scouting, Patrolling, and Sniping

TO&E 7-17, 26 February 1944