Each type of unit in the United States Army had an authorized Table of Organization and Equipment that showed, in charts

• Smaller sub-units

• The number of men, their ranks, their Specification Serial Numbers, and their MOS

• The number or ratio per men of pieces of equipment, weapons, or vehicles assigned to the unit.

• Notes and the men's relationship to the vehicles, weapons, and equipment, where relevant.

Nicely copied eamples of WWII-era US TO&Es can be found here

In the US Army, mismatches of men and equipment tried to be avoided as much as possible by following the tables, but they still happened due to the reality of combat. Groups of several infantry or armored divisions were served by a replacement battalion that operated several miles behind the divisions' rear echelon and moved with them. Men would first arrive from taking their training in the United States to England or sometimes France directly, and then proceed to one of the Field Army replacement depots, and then on to an intermediate depot before being assigned and going to the divisional replacement battalion for final placement. It was imperative that division personnel officers or others knew their situation and followed the appropriate tables when selecting replacements from depots for their unit, or else snarls could result.

The replacement depots were often lonely places; men had no unit "identity" yet, and were herded around impersonally like cattle, stuck in the depots until being selected by a unit that needed replacements. This often took several weeks. Many veterans (by the fall of 1944 there were few) of the earlier campaigns in France harbored a firm distrust or distanced themselves from replacements, taking an "I don't know him and don't want to know him, he's just going to get killed anyway" attitude.

In some cases, replacements could be brought up to the front the same day or the day after a given loss occurred depending upon whether the replacement system was "flowing" properly at that point in time or if the situation was urgent enough. In other cases, replacements had to be brought up after a battle; the unit receiving them would be shorthanded (often severely) for a time while moving to a rest area in the rear or another sector and getting settled. After the Hürtgen Forest battles, a point was sternly made by several division and corps studies not to bring marginally trained^a replacements up to the front lines during a fierce battle, as they would only become exhausted or get killed quickly due to their unfamiliarity with combat.

In contrast to soldiers, replacements for heavy vehicles such as tanks could not be brought up during the heat of battle, and often had to wait until the unit was not engaged in combat or pulled back. New tanks came from the United States and migrated into each field army's Ordnance pool. From there, they were "unpacked" by Ordnance Maintenance or Evacuation units and were taken to each battalion's designated "receiving" area by heavy tank transporters. Special" vehicles like the M29 Weasel tracked cargo carrier were also kept in the Ordnance pool, to be issued to units as needed.

During the period when units were operating shorthanded due to losses, "excess" crews who lacked vehicles, if they were not injured, were usually used for other purposes within the unit, such as litter bearers, truck drivers, assisting other personnel like quartermasters or mechanics, or acting as scouts or advisers for newly-arrived crews.

Often, replacements for given vehicle losses incurred in a time period (say, a month) could not be given to a unit in a timely manner or all at once, and had to be given singly or in several groups, sometimes weeks apart, as the Ordnance replacement pool could not "catch up". As a result, armored units often operated slightly understrength for most of their time in service after entering combat. Maintenance also became an issue. After the dash across France in August and September 1944, the 3rd Armored Division stopped to catch its breath at the German border and found that only 75 of its medium tanks (out of 232 authorized) were capable of participating effectively in combat.

Later in the war, armored units sometimes got large numbers of newly issued tanks to replace their old ones; the old tanks were sometimes retained for other purposes, such as training replacements. Fighter groups usually did the same thing, keeping a few old planes as "hacks" to train pilots or use for cargo or pleasure flights. The 752nd Tank Battalion in Italy re-equipped with a full complement of 53 M4A3(76) Sherman tanks by spring 1945 and put their 39 old M4 and M4A1 Sherman tanks in reserve.

For the spring 1945 offensive, a platoon of the new 76 mm Shermans were withdrawn from each company and replaced with a platoon of the old tanks for use as "point" tanks when crossing mined areas, to avoid damaging the new tanks. One tank commander went in alone and lost five of the old tanks probing a minefield, each time returning to pick up a new one.

a: In contrast with the specific and combined-arms training offered to soldiers assigned to an infantry or armored division from the very beginning of their service, US Army replacement training focused upon giving all replacement soldiers general military training ("soldiering") and experience with a variety of weapons and tactics. They would receive more intensive training for their specific role at a replacement depot or battalion or at the front; sometimes, this training was a bit shoddy

Sources:

A Dark and Bloody Ground: The Hürtgen Forest and the Roer River Dams 1944-1945, by Edward G. Miller

The Guns at Last Light: The War in Western Europe 1944-1945, by Rick Atkinson

The Day of Battle: The War in Sicily and Italy 1943-1944, by Rick Atkinson

Various tank battalion after action reports

Sherman Minutia Website