Croatian has 7 cases. Each of them replies on specific questions. About questions you can read here:
http://learn-croatian.com/grammar-cases.php
Usually we put questions for instrumental "with whom", "with what" but often instrumental comes without "with" which is translated like "s" or "sa".
Let's see some examples (for instrumental):
We write with pencil. (We write WITH WHAT (with pencil)) - Pišemo OLOVKOM.
Olovka - singular, feminime, nominativ --> s, f, N
I come with friend (I come WITH WHOM (friend) - Dolazim S PRIJATELJEM.
Prijatelj - s, m, N
Prijateljica - s, f, N
Without preposition "s/sa", instrumental can be:
1. adverb of place
Hodam ULICOM (I am walking by street)
ulica - s, f, N
2. adverb of time
Ne radimo NEDJELJOM (We don't work on Sunday)
nedjelja - s, f, N
3. attribute
Promet se odvijao ŽELJEZNICOM (Traffic went by railway)
željeznica - s, f, N
and so on...
I don't see any easy way to learn cases. Comparing them? I'm not sure what to answer on this because every case has function for himself.
Here is declination of girl's name Lara:
Nominativ: I am LARA
Genitiv: There isn't LARE
Dativ: I'm taking this to LARI
Akuzativ: I see LARU
Vokativ: Hey, LARA (or LARO) - mostly depends on different parts of Croatia
Lokativ: I'm talking about LARI
Instrumental: I'm coming/going with LAROM.
You should have in mind that this is example with feminime noun (in singular) which in nominative ends with vowel. Endings are not the same with feminime nouns which in nominative form don't end with vowel.
Example with noun Ines (girl's name which doesn't end with vowel):
N: I am INES
G: There isn't INES
D: I'm taking this to INES
A: I see INES
V: Hey, INES
L: I'm talking about INES
I: I'm coming/going with INES
Also, there are musculine form and neuter, both with forms that end with vowel and without them. Plus singular and plural.