Eid al-Fitr lasts for just one day, which is the first day of Shawwaal.
With regard to the commonly-held belief among people, that Eid al-Fitr lasts for three days, this is merely a custom that is known among the people, and has nothing to do with any shar’i rulings.
Al-Bukhaari (may Allaah have mercy on him) said:
Chapter: Fasting on the day of al-Fitr.
Then he narrated (1992) that Abu Sa’eed (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) forbade fasting on the day of al-Fitr and al-Nahr.
Based on this, the day of al-Fitr is just one day, on which it is haraam to fast, As for the second and third days of Shawwaal, it is not haraam to fast those days; it is permissible to fast it to make up a missed Ramadaan fast or as a voluntary fast.
And Allaah knows best.