Just like in English, the word “to order” can have several quite different applications in German:

– “bestellen”: This word is used for arranging that something is delivered, brought or reserved:
“Ich möchte eine Salamipizza bestellen.” – “I would like to order a pepperoni pizza.”

– “ordnen”: This word is used in the sense of “to sort”, in essence to arrange something to give it proper structure or sequence, and its cousins “Ordnung” (f.) (“order”) and “ordentlich” (“orderly/neat”) are, to put it mildly, quite common in German:
“Ich ordne die Ordner ordentlich für das Ordnungsamt, in Ordnung?” – “I am sorting the folders neatly for the public order office, all right?”

– “anordnen” / “beauftragen” / “befehlen”: Respectively, these words mean “to direct”, “to instruct” / “to assign”, and “to command” (in an authoritarian or military manner):
“Ich habe ihn beauftragt alles zu erledigen.” – “I instructed him to finish everything.”