In "All Quiet on the Western Front" the protagonist serves as a private for 5 or 6 whole years during the First World War and is never promoted. Was it common? What did he have to do to be promoted?

Men both starting and ending their service as privates or other low ranks is not uncommon. It happens much more often in wartime, when the military is very small in peacetime, or when it is forced to expand massively in a short period of time. Promotion to the next rank after a specified period of time, such as six months, did not exist in many militaries, or did not come about until recently. In war, some men are good soldiers, but are simply "forgotten" in the bureaucracy.

The German Empire utilized conscription, with men entering active service for two years at the age of 21, although they could join the Landsturm at 17. Military service for ordinary males around the time of World War I could last then, in most cases, for a maximum of 26-29 years either in an active, reserve, or militia component. It was uncommon for a short-term conscript musketier, infanterist, or soldat (private) to be promoted; non-commissioned officers above the rank of gefreiter (roughly equivalent to private first class or lance corporal) were drawn from a pool of career soldiers who had volunteered for active duty beyond their initial term, and their promotions strictly scrutinized by their commanding officers until vacancies appeared. Promotions from the enlisted ranks to the officer corps did not exist until 1918.

Component	Ages
Landsturm	17-20
Stehendes Heer	21-22 (half)
Ersatzreserve	21-22 (half)
Reserve	23-27
Landwehr	28-37
Landsturm	38-45

The below part of the answer applies to the United States in World War I, the interwar period, and World War II, although the same general idea could be applied to France, Germany, Russia, the United Kingdom, or any number of major powers.

Each unit in the United States Army operated (and still operates) under what is most commonly known as a table of organization and equipment (although other names were used for it in the past). The table of organization and equipment of a unit, taking into account its tactical or strategic function, lays out its organization, the number of men assigned to it, their roles and allowed ranks, and the amount of equipment assigned to each man or to the unit as a whole.

For each unit the T/O&E prescribed the number of its officers and men, the grade and job of each, the proportion of various occupational specialists, the arrangement of command and staff and administrative personnel, the means of transport and communications, the provisions for supply, maintenance, construction, and medical care, and the kind and quantity of individual and unit armament, together with the relationship between supporting weapons and consequently the tactics of the unit.

Here is the table of organization and equipment of an American rifle company, adopted in 1918

During the interwar period, promotions in the small U.S. Army were uncommon due to the parsimony of Congress and the stranglehold of the Great Depression. It was common, especially in the National Guard of the United States, to let underage men of fifteen or sixteen in; it often guaranteed for the Depression family at least some money each month.

Here is the table of organization and equipment of an American rifle company, adopted in 1944

The table of organization and equipment lays out specifics in regards to rank and the roles men performed based upon that rank. If a man was promoted to a rank above what his old position dictated in the table of organization and equipment, he would need to be re-trained to fill his new position, and possibly take on a different role. If there were no vacancies available in a higher position that a man could reasonably be re-trained for, he would not be promoted, at least until a vacancy opened. Exceptions to this rule include battlefield promotions, either out of necessity, or out of action; if a man distinguished himself in combat and there happened to be an un-filled vacancy, he would be promoted and re-trained instead of a replacement of a higher rank being requisitioned and assigned.

The table of organization and equipment also lists the number of "allowed" ranks in an organization. The 1944 American rifle company of 193 men "allowed" a maximum of one captain, three first lieutenants, two second lieutenants, one first sergeant, four technical sergeants, sixteen staff sergeants, fifteen sergeants, one corporal, two technicians grade 4, four technicians grade 5, 40 privates first class, and 104 privates. The privates first class were 28 percent of all privates, and hence promotions could occur up to a maximum of 40 out of 144, if the table of organization and equipment was followed to the letter (which it often was not).

The use of individual replacements in the U.S. Army also intervened to make promotion more uncommon. If Sarge or Lieutenant became a casualty, Private Doe often wouldn't be promoted, and a replacement would be brought in. Promotion from the enlisted ranks, particularly "low" ones, directly to the officer corps in combat during World War II was a celebrated event in unit journals, with formal ceremonies often taking place. Mass promotions also took place, if only to bring the unit into closer conformation with the table of organization and equipment it was operating under. Soldiers could be promoted while away from their unit, such as while being held as a prisoner of war or recovering in a hospital.

Sources:

Company morning reports, 134th Infantry Regiment, 35th Infantry Division

Palmer, Robert R. Army Ground Forces Study No. 8: Reorganization of Ground Troops for Combat. Washington: Historical Section, Army Ground Forces, 1946.

Thomas, Nigel. The German Army in World War I (1): 1914–15. Oxford: Osprey Publishing, 2003.

United States Army in the World War 1917-1919: Organization of the American Expeditionary Forces, Volume I. Washington: United States Army Center of Military History, 1988.