Let’s look at the use of above mentioned prepositions in the context of time. All are used to denote time but there is a difference.

At This is used for indicating the time of the day .For instance at 5PM, at 6’O’ clock etc.
 I got up at 6 am today
 She normally leaves for work at 10 ‘o’ clock in the morning.

On This is used for indicating day and date. For example on Monday, on 7th June etc.
 India got independence on 15th August 1947
 The result of the general elections will be announced on 16th May.
In This is used for indicating the month and year. For example in January, In 2014 etc.

 Usually, the Monsoon arrives in June every year.
 The next Olympic games will be held in 2016