Where exactly should the verb be?
I've come across multiple instances of the verb being placed either at the end of a sentence, or after the subject (the person that does it).
I'm not sure when to use either of these, could someone explain
Upon searching the subordinate clause, I came across a long list of words that indicate it (like after, though, than, that).
So in any sentence that doesn't include these words it goes subject-verb, but a sentence does include them then the verb is said at the end?
No, sorry, in a main clause you can have verb+subject. : "Ich habe gestern ein Buch gekauft."<>" Gestern habe ich ein Buch gekauft." Content the same, order different. It is a rule actually: when the subject is not on the first place of the sentence, subject+verb is reversed to verb+subject.
This page has a great, detailed lesson on German sentence structure: http://www.deutschseite.de/grammatik/satzstellung/satzstellung.html