“Hi brothers, I want to ask about Eid prayer, one of my friends couldn’t get to Eid prayer on time. When he arrived to the place where every one was praying, other Muslims were praying the second rakaat. He didn’t know when the Imam finishes the second rakaat what to do about the first rakaat. I think it should be different with the normal pray we do. Please tell me what he could do at that time?”
The person who arrives late to Eid Salah should complete what he has missed according to the way that he missed it. This is true for any prayer.
For example: if a person has missed the first rakaat, he should join in with the imam as soon as possible and complete the second rakaat with the imam. When the imam finishes the prayer and turns his head to the right announcing “Assalamu alaikum wa rahmatuhullah”, the person who has missed the first rakaat should not turn their head with the imam, but stand up and finish (on his own) what he has missed without breaking the salah.
Narrated Abu Umayr ibn Anas: Abu Umayr reported on the authority of some of his paternal uncles who were Companions of the Prophet (pbuh): “Some men came riding to the Prophet and testified that they had sighted the new moon the previous day. He (the Prophet), therefore, commanded the people to break the fast and to go out to their place of prayer in the morning”.
Here we can learn that if a person misses Eid prayer and it is too late to perform it, then he should complete it the next morning.
For more information on the fiqh of Eid, see here.
 Sunan Abu-Dawud