From the thesis linked by CGCampbell, American anti-tank doctrine was based around dealing with concentrated groups of German tanks on the offense, ie. a repeat of the invasion of France. To deal with this, dedicated anti-tank battalions were formed of tank destroyers: heavy anti-tank guns mounted on lightly-armored mobile platforms.
The thesis cites Field Manual 18-5 of 1942, Tactical Employment, Tank Destroyer Unit for doctrine. According to it, the basic procedure was that most tank destroyers should be held in reserve, to be committed in battalion strength when a concentrated group of enemy tanks was identified. Combat tactics were hit-and-run or ambush-based: since the tank destroyers were fragile, mobility, visibility, and superior intelligence were to be used to attack while not being attacked in turn.
In general, this doctrine was ignored. German tanks were rarely found in the massive concentrations envisioned, and as a result, tank destroyers were deployed in small groups and treated as "fragile tanks" to directly support infantry. In general, German tanks were deployed in platoon-scale or smaller units, and were dealt with by ground-attack aircraft (#1 cause of combat losses) or towed anti-tank guns (#2), with other methods (tanks, tank destroyers, infantry anti-tank weapons) seeing use only when those were unavailable.