Questions & Answers about Nach dem Spaziergang waren wir müde.
Why is it waren wir instead of wir waren?
German strictly follows the verb-second (V2) rule in main clauses. Because the time phrase Nach dem Spaziergang takes up the first position, the verb waren must come second. This pushes the subject wir into the third position.
Why does the sentence use dem Spaziergang instead of der Spaziergang?
The preposition nach always triggers the dative case. Since Spaziergang is a masculine noun (der Spaziergang), its definite article changes to dem in the dative.
Would it be wrong to say ... sind wir müde gewesen instead of ... waren wir müde?
It would not be grammatically wrong, but it sounds unnatural. Even in casual spoken German, which normally uses the conversational past (Perfekt), the verbs sein (to be) and haben (to have) almost always use their simple past forms (waren and hatten).
What is the difference between ein Spaziergang and just walking in general?
Der Spaziergang specifically refers to a leisurely walk or a stroll, usually done for pleasure or fresh air. If you are just talking about the physical action of walking to get somewhere, you would simply use the verb gehen.