What are the rules for conjugating adjectives like "Gut" , i.e. when do you use "gut" "gute" "guten" "guter"?
It depends on the case system. German has four cases. Nominative, Accusative, Dative, Genitive
First it's important to say that if a definite article is used (the=der,die,das) then the following adjective will always end in e in the nominative case.
The original adjective is "gut" so the four cases change it.
Nominative makes it er-masculine, e-feminine, es-neuter. Der gute Hund, Ein guter Hund
Accusative is just like the nominative but it makes masculine nouns en as well as the adjective. Er liebt den guten Hund. Sie kocht die gute Nudeln.
Dative is pretty different, but easy. All endings end in "en". Er spielt mit dem guten Kind. Sie liegt mit der guten Katze.
Genitive you won't really need it much until you get to an advanced level. I haven't even needed that yet.