To show something belongs to someone

The student’s notes (one student)

The students’ notes (more than one student)

The children’s toys (plural that doesn’t end in s)

To introduce a list. 

Students are expected to: Attend lectures, write in an academic style, meet deadlines and study independently.

To mark a pause in a long sentence, such as where you would take a breath when speaking.
He explained to all his tutors that he couldn’t attend lectures on a regular basis, but little could be done to accommodate him.

To separate items in a list.
He had problems with punctuation, referencing, time-management and writing effectively.

After words like however, nevertheless and surprisingly.
However, the Academic Skills Learning Zone proved very helpful.

To signify ‘extra’, information is being given
His wife, who he had met on holiday in Italy, had been married twice.

After words like states, argues and says.
As Todd (1998) argues, education is the key.

To show you are directly quoting someone’s words.

As Baker (2012) states, “learning is fun”.

At the end of a sentence
He left home to study at university.

To signify an abbreviation
Etc.  e.g. et al.

To introduce the second half of a sentence which expands the first half
At the end of the day you are responsible for your work; that means no one else can take the blame if you fail.