Eid al-Fitr falls on the first of Shawwal, the day after Ramadan ends, and fasting on it is forbidden, which is the point. The festival exists as the boundary of the fast, and the prohibition marks it.
Its defining obligation is not the meal. Zakat al-Fitr is a charge payable by every Muslim, including on behalf of dependants and children, before the Eid prayer is performed. It is assessed traditionally as a measure of staple food, dates, barley, wheat, rice, depending on locale, or its cash equivalent, and it is due from anyone who has food beyond their needs for the day, which means it is owed by nearly everyone rather than only by the wealthy. The stated purpose in the hadith literature is to purify the fast of lapses and to ensure that the poor can eat on the festival day. Its timing is the operative part: it must reach recipients before the prayer, not afterwards.
The Eid prayer itself is congregational, held in the morning, traditionally in an open space rather than in a mosque, and preceded by taking a bath, dressing well and eating something, again the deliberate breaking of the fast pattern.
The customs beyond that are regional and extremely varied: specific sweets in Turkey, Indonesia and South Asia, new clothes, visits to graves, money given to children. The festival is called by different names in different languages, the Sugar Feast in Turkish, Lebaran in Indonesian, Hari Raya in Malay, and the local shape of it differs more than the shared name suggests.