I understand the meaning of each auxilary verb (and their grammatical usages) but when do you use each in practice. For example: “Sie ist gestern nicht mitgekommen.” I get that “mitkommen” is an intransitive verb, so if you use an auxilary, you’d use forms of “sein,” but why in this form (ie, why not “Sie kam gestern nicht mit”). Alternatively, why would you not use an auxiliary in this sentence: “Das wusste man früher allerdings nicht.”
“Sie ist gestern nicht mitgekommen” and “Sie kam gestern nicht mit” are two different tenses (Perfekt and Präteritum), while they have the same core meaning ("she did not come a long") they are used in different contexts.
It is similar in a lot of ways, but not exactly the same, as the English present perfect ("she has come along") and simple past ("she came along").