Salutes by Individuals & Units in Formation; 
Obligation to Salute
From Der Rekrut

If the soldier is prevented from saluting because he is carrying or holding objects, etc., the salute is indicated by walking past at attention & standing or sitting at attention.  Saluting while seated is allowed only if circumstances require it or if the salute cannot be given while standing, e.g., in an enclosed vehicle, in open moving vehicles, etc.  In all other cases, subordinates are required to stand while saluting.

Enlisted men must also salute uniformed civilian Wehrmacht officials, as well as military chaplains in vestments, including former officials of the Wehrmacht, the old army & the old navy who are in uniform.

All salutes should be quickly & crispy executed.  They begin five steps in front of the superior & end two steps past, or are given upon entering & leaving a room.

In rooms inside of barracks (including the canteen), official buildings, or other accommodations, the command for "Attention!" shall be given by the duty officer, etc., when officers & platoon sergeants (company sergeants) enter their own company's space, etc.  Everyone stands at attention facing the superior until the superior says "At ease!"  or leaves the room.  The person of most senior rank announces the superior.  In offices, "Attention!" is not commanded & the superior is not announced.  Salutes are performed from the seated position, as long as the superior does not speak to the subordinate.

In enclosed spaces other than barracks, such as public transportation, waiting rooms, boarding houses, garden cafés, theaters, concert halls, & lecture rooms, a salute is to be given if a superior & a subordinate approach within greeting distance of each other.  The salute should be performed as appropriate to the circumstances.

Whoever is the first to notice a superior informs his companions in a timely manner of the need to salute.

Before saluting, remove cigars from your mouth, hands from your pockets, etc.  Offering a greeting with a whip or similar item in the saluting hand is not permitted.

When on horseback, perform the salute at a walk if a duty-related task does not prevent it.  Subordinates wishing to overtake a superior on horseback must ask permission to do so (except during field exercises, maneuvers, etc.)  Cyclists, drivers, & riders salute by sitting at attention.

For marching units on horseback or in vehicles, the command to salute is "Attention!  Eyes right (left)!"  When "Attention!" is heard, sit at attention as prescribed.  When the command "Eyes right (left)!" is given, personnel in the back seat of a vehicle turn their heads & look to the opposite⁴ side.  The salute ends when the command "Ready, front!" is given.

Marching units with vehicles salute upon a sign from the commander, which is to be repeated by any accompanying personnel except the driver of the vehicle.

For units on foot that have halted, the commander says "Attention! Eyes right (left)!"  For units on horseback or in vehicles that have halted, the command is [also] "Attention! Eyes right (left)!"  Look at the superior officer.  If he is walking or riding along the unit, every head should be turned toward him & every gaze should rest on him until he is two steps past, then the head & eyes should automatically face forward.  If units are dismounted, they step to their horses or vehicles when the command "Attention" is given.  The leaders go to their prescribed positions.  The salute ends when the command "At ease!" is given.

Units in formation without headgear give the same salute as those with headgear.  However, in this case, the unit commander gives the German greeting if he is also hatless (in a sports uniform, for example).  

Wehrmacht personnel to whom no salute is owed by the unit in formation are merely saluted or greeted by the commander.  When marching with the route step (or when at ease), any soldier is free to greet civilians.
 

For soldiers in uniform & wearing headgear, the type of salute to use is summarized in the regulations on saluting.

Soldiers in uniform who are not wearing headgear or who are dressed in civilian clothes use the German greeting.

The soldier with a lower rank or less seniority should salute first.  It is a matter of honor among soldiers - even if the person who is being saluted is not part of the Wehrmacht - to execute each salute in a crisp & soldierly manner.

Under the same conditions discussed previously, the obligation to salute does not apply to certain individuals (e.g. drivers of motor vehicles, mounted messengers, etc.)

A voluntary salute is expected when members of foreign armed forces salute first.  Units in formation do not salute.  If a salute is to be given, the senior officer of the post or the naval commander will so order.

If a superior returns a soldier's salute by answering "Heil!" or "Good morning," etc., the greeting is answered using the same wording & adding "(superior's rank), Sir!"  

Superiors greet units in formation by saying "Heil!" & adding the branch of service or force.  The unit answers "Heil!" & adds "(superior's rank), Sir!"  The Minister of War is answered with "Heil, General, Sir!"  The Fuehrer & Chancellor of the Reich is answered with "Heil to the Feuhrer!"

¹  Following the July 20th assassination attempt on Hitler, the military salute was changed.  The traditional "Military Salute" of the hand to the cap visor or rim of the helmet, was then forbidden.  The "German greeting" or "Party salute" was ordered to become the official salute of the Wehrmacht.  Many soldiers viewed the "German greeting" as ridiculous & impractical.  One veteran commented that after this new order, "it was not uncommon to observe entire companies carrying their mess tins in their right hands to avoid being compelled to demonstrate their 'loyalty to the party.'"
²  "German greeting" (Deutscher Gruß) - the German name for the Nazi salute [Translator]. Even though this was an official regulation, it is advised that reenactors do not do this salute due to its political affiliation. 
³  "Parade-stepping" (Exerziermarsch) - the German name for goose-stepping. [Translator]
⁴  "Opposite side" - Apparently, passengers in the rear seat faced in the opposite direction [Translator]