How were the German people introduced to the concept and etiquette of the Nazi salute and the proper usage of "Sig Heil" and "Heil Hitler"?

The 'Nazi salute' is mostly thought to have first originated from the gesture of the 'roman saute'. While there isn't any historical Roman texts or artworks depicting the salute it's largely thought to have originated from the Roman Empire. The painting 'The Oath of the Horatii' by Jacques-Louis David (1784) is probably the starting point of what we identify as the Roman salute. Many neo-classical artworks and sculptures developed the identification of the gesture aswell. So pop-culture had a big part in the identity of the gesture. In 1914 the gesture was included in the silent film 'Cabiria'. The screenplay of the film was written by Gabriele D'Annunzio, an Italian who lead a career in Italian politics who adopted the salute. D'Abbunzo was a ultra-nationalist, so when the fascist party came around Benito Mussolini adopted it, as ultra-nationalism in Europe was usually synonymous or alike with Fascism. The connection between Rome and Fascism is because both started in Italy. Now getting to the Nazi part. The Nazi Party were National-Socialist, an off branch/depiction of fascism, so many members of the party would use the gesture because they shared the same ideologies and ideas. The gesture started to gain alot of popularity as it was shown about quite a bit. The Nazi Party during 1924 made the word's "Heil Hitler" compulsory when doing the salute as a display of commitment to the party. The oral greeting of "heil" became popular earlier in the pan-German movement around the year 1900. Pan-Germanism was a movement which advocated the unification of all countries who spoke German, which is also what Hitler advocated and wanted. "Sieg Heil" is a paraphrased version of "Heil Hitler", so each would be used differently depending on the situation and context. After 1933 the Nazi Party started to bind the salute by law. In a decree in 1933 one day before the ban on all non-Nazi parties, all German public employees were required by law to use the salute when appropriate, as well as doing it while singing the national anthem. By 1933 the salute was very popular, and became an ordinary gesture and way of life, like saying "hello" or waving for example. Postmen for example would use the gesture when knocking on peoples doors to deliver packages or letters. Metal signs advising people to use the salute in public places were also placed on telephone poles and street lights. The oral greeting "Heil Hitler" also became very ordinary, it was popularly used as a greeting aswell, most greetings would go "Heil Hitler, how are you today? (Heil Hitler, wie geht es Ihnen heute?") In the Nazi education programs children were also taught to do it, it was implemented into fairy tales and classics aswell such as 'Sleeping Beauty', and students would do it to adults passing in and out of rooms, aswell as doing it during the beginning and ending of the day. During the Berlin Olympics some athletes (those German or those not) used the salute in the opening ceremony when passing Hitler, aswell as by delegates from Bulgaria, France, Iceland and Turkey to name a few. Because of the constant use and sight of it, it was very common for people to start learning it and start using it themselves.

tl;dr, Basically the Nazi Salute originates from the Roman salute, this was often portrayed in pop-culture and was eventually adopted by politicians. Other leaders started using it because they were connected in terms of ideology. The use started to become more widespread because of popular support for fascist parties, so the Nazi Party started putting regulations on the use of it, binding citizens by law to do it. Education programs and mass use influenced almost everybody in Nazi Germany to start using it. Etiquette was learnt/explained/educated by first hand experience as well as by the law and education programs

I hope this answers the question OP, sorry for the long history catch up.