Memorise this rule:

At a time, On a day, In a period
 
AT a time       (times: 10 o'clock, 5:30, etc.)
ON a day       (days and dates: Monday, Thanksgiving, the 5th of June, etc.)
IN a period    (periods of time: week, month, year, 4 hours, morning, etc.)
 
AT
I get up at 9 o'clock
I was there at noon (noon= 12:00 pm)
You can come at lunch time
 
ON
I went to Berlin on Monday
I was born on May 2nd
My brother arrived on Christmas Day
 
IN
He was born in the 19th century
She had her holidays in June
Don't go to Egypt in summer
 
  IN can be used in two other special cases:
1- To say how soon something will happen
- I'll see you in two days (also: ...in two days' time)
- come to see me again in a week  (also: ...in a week's time)
2- To say how long something takes to happen
- I can run 200 metres in 30 seconds
- he wrote a book in a month

EXCEPTIONS
 
1- We say "in the morning", "in the afternoon", "in the evening", but: "at night". The expression "in the night" means "during one particular night". Compare:
- Don't go out at night, it can be dangerous
- We slept in a tent, but I woke up in the night and could only sleep two hours
2- at the weekend / at weekends (AmE: on the weekend)
3- on holiday
4- ON + day + part of the day
- I went there on Monday morning
- Come with us on Saturday night
- We get our presents on Christmas morning
5- We say: In the past, in the future, but... at present
6- Christmas, Easter and other long holidays use On for the day but AT for all the period
- Come and see us on Christmas Day (December 25)
- I stayed at home at Christmas (all my Christmas holidays)
- We're going to Zamora at Easter
- What are you doing on Easter Monday?
 
Note: when talking about Dec 25, American people say "on Christmas" or (less often) "on Christmas Day", but in British English we only say "on Christmas Day".
"At Easter" is the same as "In the Holy Week" (less often). "On Easter" is the same as "on Easter Sunday".  For the other days of Easter we must specify: on Easter Monday, etc.

When we say next, last, this, every we do not use at, in, on.

I went to Paris last summer (not: in last summer)
I'm starting my holidays next Saturday (not: on next Saturday)
I go home every Easter (not: at every Easter)
We'll call you this afternoon (not: in this afternoon)