How would, say, a Finnish or American volunteer be taught German?

As per an older answer of mine:

There are two publications that I am aware of that aim to teach foreign soldiers the German language, or more precisely, a basic understanding of German military vocabulary.

These are the Bildsprecher Deutsch für Soldaten: Grundausbildung and Bildsprecher Deutsch für Soldaten: Sonderausbildung.

As you can tell from the covers, these publications rely rather heavily on drawings to get their message across.

The books both open with the following introduction (translated):

In war, many who do not speak German must become soldiers. [...] During the war there are no language teachers nor long moments of learning, instead, eight weeks parallel with basic training must suffice to teach the common language of regular service.

The Grundausbildung booklet is the "basic training" version, which explains the basic equipment, internal service (i.e. life in the barracks), the parts of the Gewehr 98, Maschinengewehr 34, Pistole 08 (Luger), ranks, a very basic scheme of organisation, closed order drill, terrain features, squad tactics, and some combat basics.

To give an example of the basic nature of it, the page on the Gewehr 98 has the following words on the left side of the page:

Firearm

Rifle

Carbine

Muzzle

Front sight (post)

Barrel

Cleaning rod

Rear sight (notch)

Sight (2+5)

Bolt

Trigger

Sling

Stock

Not exactly a degree in mechanical engineering, but rather a basic understanding of firearms parts.

The second booklet, Sonderausbildung (Special training) goes into more depth with the particular Waffen (Artillery, tanks, supply, medical).

Similarly, the parts of a tank are described using drawings as such..

Sources

Bildsprecher Deutsch für Soldaten: Grundausbildung, Dr. Wilhelm Bode, Otto Schwartz & Co Verlag, 1944

Bildsprecher Deutsch für Soldaten: Sonderausbildung, Dr. Wilhelm Bode, Otto Schwartz & Co Verlag, 1944