Fasting is forbidden on this day, as it marks the end of the month long fast of Ramadan.
Abu ‘Abaid (the slave of Ibn Azhar) said:
"I witnessed the 'Id with 'Umar bin Al-Khattab who said, "Allah's Apostle has forbidden people to fast on the day on which you break fasting (the fasts of Ramadan - Eid ul-Fitr) and the day on which you eat the meat of your sacrifices (Eid ul-Adha)." (al-Bukhari)
No sunnah prayer may precede or follow the Eid prayer - except if it is performed in a masjid instead of the musallaa, in which case one must pray two Rak`aat before sitting down. Ibn `Abbaas narrated:
"The Prophet went out (of his house) on the day of Fitr, prayed two Rak`aat, and did not pray before or after it." (al-Bukhari)
People sometimes spend extravagantly during Eid ul-Fitr. Allah (subhanahu wa ta'ala) says:
"Do not waste your wealth senselessly. Those who spend wastefully are the brothers of the Shaytans; and the Shaytan is ever ungrateful to his Lord." (Al-Isra Verses 26-27)