However my problem is, that I really don't know how and when to use declensions other than locative and nominative nouns and adjectives.
I'm afraid, there's no easy rules to explain it.
But at your level, you should only remember that the case depends on 2 factors:
1. All transitive verbs require their objects to be in particular case. YOU MUST LEARN THEM BY HEART. This means that when you learn a new (transitive) verb you must also learn the case it requires for the object.
In most cases it would be Accusative or Genetive for the direct object and Dative for the indirect object.
2. All prepositions require particular case(s) of the nouns they are standing before. YOU MUST LEARN THEM BY HEART. Every time you learn a preposition, besides its meaning you must also remember the case(s) i requires.
Sometimes you may notice that a proposition has several different meanings and requires different case for each one meaning e.g.:
w + locative = in
w + genetive = into
1+2. Some verbs require their object to be in particular case and to be prepended by a preposition. YOU MUST LEARN THEM BY HEART.
śmiać się z kogoś - to laugh at someone.
So, to summarize, always learn pairs: (verb + case) or (preposition + case).
And that's it :-)
Just keep learning and good luck.