That was originally called 'Toshigomori[年籠り（としごもり）]' and it was a ceremony that a family head stayed at a shrine for praying from the night of Ōmisoka[大晦日（おおみそか）](New Year's Eve) to Gantan[元旦（がんたん）](the morning of January 1st).
When going to Hatsumōde, people bring old amulet and Hamaya[破魔矢（はまや）](arrow-shaped charm for expelling evil) and leave them at the shrine or temple and buy a new amulet, etc. And they write a wish on Ema[絵馬（えま）] which is a wooden plaque for dedicating to a shrine or temple.
Meiji Shrine[明治神宮（めいじじんぐう）] in Tokyo is the most popular Hatsumōde spot and about three million people visit there at the time of Hatsumōde. And Shinshō-ji Temple[新勝寺（しんしょうじ）](Chiba), Kawasaki-daishi Temple[川崎大師（かわさきだいし）](Kanagawa), Sensō-ji Temple[浅草寺（せんそうじ）](Tokyo), Sumiyoshi Shrine[住吉大社（すみよしたいしゃ）](Osaka) are popular.