If someone joins Eid Salah after its Jama’at has begun, then there are different ways of how to offer the rest of the Salah:
1 If he joins Salah in the first Rak’at after the Imam has uttered the Takbeers, he should utter three Takbeers (in addition to Takbeer Tahrimah) at the same time, even if the Imam has started the Qira`at. (He should also raise his hands up to his ears for all three Takbeers.)
2 If he has not uttered Takbeers yet and the Imam has gone in Ruku’, now he should not utter the Takbeers in the standing position, rather he should go in Ruku’ with the Imam and utter Takbeers in Ruku’.
3 If he finds the Imam in Ruku’ and has a strong presumption that he will catch up with the Imam in Ruku’ after uttering Takbeers (in standing position), in this case, he should utter Takbeers in standing position and then go to Ruku’; otherwise, he should go to the Ruku’ after uttering ‘اَللہُ اَکْبَر’ and utter three Takbeers in Ruku’. If he had not completed the Takbeers in Ruku’ and the Imam raised his head, then the remaining Takbeers have now become annulled (i.e. he shall not utter the remaining Takbeers now).
4 If he joins Salah after the Imam has stood up from Ruku’, then he should not utter the Takbeers now, rather he should utter (the missed) Takbeers when he offers his (remaining) Salah (after the Imam has completed the Salah).
5 If he joins in the second Rak’at, he should not utter the Takbeers of the first Rak’at now, rather he should utter them when he stands up to offer his missed Rak’at. If he gets the Takbeers of the second Rak’at with Imam, it is better, otherwise it also has the same ruling that has been mentioned for the first Rak’at.
Note: Do not raise your hands where it is mentioned to utter Takbeer in Ruku’. (Durr-e-Mukhtar, Rad-dul-Muhtar, vol. 3, pp. 64-65; Fatawa Hindiyyah, vol. 1, pp. 151; summarized)
Read the booklet of Shaykh-e-Tareeqat, Ameer-e-Ahl-e-Sunnat دَامَـتْ بَـرَكَـاتُـهُـمُ الْـعَـالِـيَـه namely, ‘Namaz-e-Eid ka Tareeqah’ [Method of Eid Salah], in order to know the complete method of Eid Salah and its rulings.