بسم الله الرحمن الرحيم
In the Name of Allah most Gracious most Merciful
Eidul Adha (عيد الأضحى) is the second celebration after Eid Al Fitr (عيد الفطر). It starts on the tenth day of the twelfth month of the Hijri calendar. The best act of this Eid, is the sacrifice. The time of Udheyyah (الأضحية) is from after the Eid salat until the end of the days of Tashreeq (أيام التشريق).
Anyone who is able to sacrifice should. The sacrifice is done on four legged animals: camels, cows, sheep, or goat. It would not be valid if one sacrifices a chicken or a duck. Allah says (Surat Al Hajj Ayah 28):
لِّيَشْهَدُوا مَنَافِعَ لَهُمْ وَيَذْكُرُوا اسْمَ اللَّهِ فِي أَيَّامٍ مَّعْلُومَاتٍ عَلَىٰ مَا رَزَقَهُم مِّن بَهِيمَةِ الْأَنْعَامِ ۖ فَكُلُوا مِنْهَا وَأَطْعِمُوا الْبَائِسَ الْفَقِيرَ
That they may witness benefits for themselves and mention the name of Allah on known days over what He has provided for them of [sacrificial] animals. So eat of them and feed the miserable and poor.
Some of the meat that comes from the sacrifice should go to the poor, while one gives some to family and friends, while one keeps some for himself and his family. It is prohibited to fast on the days of Eid, for the days of Eid is for eating, drinking, and the remembrance of Allah. The Prophet (peace and blessings be upon him) said:
أَيَّامُ اَلتَّشْرِيقِ أَيَّامُ أَكْلٍ وَشُرْبٍ, وَذِكْرٍ لِلَّهِ عَزَّ وَجَلَّ
The days of Tashriq are days of eating, drinking and remembering (dhikr) of Allah, the Most Great and Glorious (Saheeh Muslim)
Eid Al Adha (عيد الأضحى) is one of two celebrations in Islam, there are no other celebrations in Islam except for these two Eids.
If you have any questions in regards to this subject, then I invite you to ask them here.
سبحان رب العزة عما يصفون، و سلام على المرسلين و الحمد لله رب العالمين