In this post, I present some useful rules for case marking (إعراب).

A definite noun with (ال) following a demonstrative has the same case, as they are substitutes (بدل), e.g.  

هذا الطالبُ جديد. (This student is new.)

تكلمت مع هذه البنتِ. (I spoke with this girl.)

قرأت هذه الكتبَ. (I read these books.)

 

An indefinite noun that follows a superlative adjective (أفعل التفضيل) is case marked as a specification (تمييز), and it is always accusative (منصوب), e.g.

الكاتب أكثر شعبيةً من الشاعر. (The writer is more popular than the poet.)

أختي أكثر اهتماماً بالعلوم مني. (My sister is more interested in science than me.)

القراءة  أوسع انتشاراً في الغرب. (Reading is more widely spread in the West.)

First, second, third, fourth, etc. are accusative (منصوب), as they are adverbials (حال).

أولاً، ثانياً، ثالثاً،  (Firstly, secondly, thirdly, etc.)

Possessive pronouns at the end of nouns do not change vowelling, but they are considered genitive (مجرور) as part of an idaafa (مضاف إليه).

كتابي جديد. (My book is new.)

هذا كتابك.  (This is your book!)

Object pronouns at the end of verbs do not change vowelling, but they are considered accusative (منصوب) as object (مفعول به) of the verb, e.g.

ساعدني أخي في الدراسة.  (My brother helped me to study.)

قابلته بعد الصف.  (I met him after the class.)

عاقبنا الأستاذ.  (The teacher punished us.)