From Nookipedia, the Animal Crossing wiki
In Animal Crossing
The event starts at 6pm and lasts until 9pm. At this time, the player can go to the town lake to watch a meteor shower. During the event, Tortimer will give the player a telescope for attending the event. During this event, there are several meteors that fly through the sky, and they are reflected off the lake, since the player cannot see the sky.
In Wild World
There are no Meteor Showers, but meteors appear randomly in all weathers between 7 PM and 4 AM in the sky. The player can wish on these stars if they press 'A' while the meteor is on screen, and are not holding a tool or umbrella. This will cause a Spotlight Item to be sent to the player's mailbox from Wishy.
In City Folk
The Bulletin Board will have a message the day of the Meteor Shower telling the player that it will occur. This time, the player cannot wish upon the stars. Meteor Showers do not appear on special dates such as during the June 16 - July 15 rainy season or certain snow days, for example.
In New Leaf
The Meteor Shower returns in New Leaf, appearing on random days when the weather is clear. They do not appear on the following dates:
If a meteor shower is to occur, a note will appear on the town's signboard between 10 and 11 AM on the day of the shower. As with Wild World, the player can wish upon a star, which is done by pressing 'A' upon hearing the twinkling sound of a shooting star. The next day, a letter will appear in the mail from Wishy with a piece of rare furniture (Spotlight Item).