It depends on which Eid you are talking about. Eid Al-Fitr comes after Ramadan, the holy month of fasting. Muslims have a small breakfast and then gather to pray Salah tul-Eid. Then, the usually go to many get togethers and just have fun and enjoy themselves.
Eid Al-Adha is celebrated in a slightly different way. After praying Salah tul-Eid, the men go (woman can go too, but they usually stay at home) and slaughter a goat, sheep, cow, chicken, etc. They may cook it that day, or keep it for later. Some give a portion of the meat as charity. Then everyone celebrates and has a good time.
In both Eids, most people wear new and beautiful clothes. They exchange gifts, especially in Eid Al-Fitr. Women will cook delicious foods, and everyone stays in a good mood.
InshaAllah this will help
1. Eid -ul Fitar: Ist of Shawal (10th month of Hijra calendar). It is celebrated as thanks giving to Almighty Allah for blessing the Muslims with the sacred month of Ramadhan in which they fasted and and did extra worship to win His pleasure.
The Muslims take bath, put on neat and neat dress, eat some sweet dish and go to Eid Gah (special mosque) to offer Eid Prayer. They also exchange gifts. It is an occasion of forgivrness and making peace. The poor are also helped with food and charity. The Muslims don't indulge in merry making. They thank Almighty Allah.
2. Eid-ul-Azha: 10th of the 12th month. Celebrated in the memory of Hazrat Abraham's nearly sacrifice of his son Hazrat Ismaiel (AS). The Muslims offer Eid prayer, thank Almighty Allah and offer animal sacrifice. It is also the next day of the chief ritual of Hajj- The Day of Arfa.