Allaah, The Most High, says:
"(He wants you) to complete the same number (of days) and that must magnify Allaah (takbeer) for having guided you and so that you may be grateful to Him." [Al-Baqarah 2:185]
Indeed it is established that the Prophet used to emerge on the day of 'Eid-ul-Fitr and say the takbeer up until he reached the musallaa and up until he had performed the prayer. So when he had performed the prayer he stopped saying the takbeer.
The scholar of hadeeth al-Albaanee said: "This hadeeth contains evidence concerning the legality of what the Muslims are acting upon, from saying the takbeer aloud on the way to the musallaa; even though many Muslims have become negligent of this Sunnah to such an extent that it has nearly become a 'thing that was'......
From that which is appropriate to remind us of at this point, is that saying the takbeer aloud does not mean that it is permitted to say it in unison, as some people do. Likewise, all other supplications in which raising the voice has or has not been prescribed, then reciting the sup plication in unison is not permissible. So be cautious of this and let us always focus our eyes upon the fact that the best guidance is the guid ance of the Prophet (SAW)." [Silsilatul Ahaudeeth as-Saheehah (1/121)]
Shaikh-ul-Islaam Ibn Taymeeyah was asked about the time when the takbeer should be recited during the 'Eids. So he replied:
"All praise be to Allaah. The most correct opinion with regard to reciting the takbeer is that which the majority of the pious predesessors, the jurists from amongst the Companions and its A'immah are upon, - that is to say the takbeer after every prayer from Fajr (Dawn) on the day of 'Arafah until the last day of Tashreeq. It is permitted for everyone to say the takbeer aloud when proceeding to the 'Eid prayer and this is agreed upon by the four Imaams." [Majmoo al-Fataawaa (24/220) and refer to Subul-us-Salaam (2/71-72)]
I say: His (may Allaah have mercy upon him) saying: After every prayer - in particular - is a matter for which there is no evidence. Rather the correct opinion is that it is at all times without particularisation.
This is inferred upon by the saying of al-Bukhaaree in the chapter on the two Eid's in his book as-Saheeh (2/461): "Chapter: Takbeer in the days of Mina and when proceeding to Arafah."
'Umar (may Allaah be pleased with him) used to make takbeer in his tent in Mina such that the people in the masjid could hear him and so they would make takbeer and the people in the market would make takbeer such that Mina would resound with the takbeer.
Ibn Umar (may allaah be pleased with him) used to make takbeer in Mina on these days, after every prayer, while reclining on his couch, in his tent, in his gatherings and when walking all in these days.
Maimoonah (may Allaah be pleased with her) would make takbeer on the day of Nahr. The women used to make takbee, alongside with Abaan Ibn Uthmaan and 'Amr Ibn Abdul-Aziz during the nights of Thasreeq with the men in the masjid.
When Ibn 'Umar (may Allaah be pleased with him) would leave (his house) on the morning of 'Eid-ul-Fitr and 'Adhaa and he would say the takbeer aloud until he reached the musallaa and then make tak beer until the Imaam came.38
The manner of saying takbeer has not been authentically reported in a hadeeth of the Prophet from that which I know, but it has been reported from some of the Companions (may Allaah be pleased with them all).
Ibn Mas'ood used to say: << Allaahu-Akbar. Allaahu-Akbar. Laa ilaaha illallah. Wa-Allaahu Akbar. Allaahu-Akbaar. Wa lillaahil-Hamd>> [ Reported by Ibn Abee Shaibah with an authentic chain of narration.]
(Allaah is the Greatest. Allaah is the Greatest. There is none who has the right to be worshipped except Allaah. Allaah is the Greatest. Allaah is the Greatest and to Allaah belongs all praise.)
Ibn 'Abbaas (may Allaah be pleased with him) used to say: <<Allaahu-Akbar Allaahu-Akbar; Allaahu-Akbar wa-lillaahil-Hamd. Allaahu-Akbar wa ajallu, Allaahu-Akbar 'alaa maa hadaana. [Reported by Baihaqee (3/315) and it has an authentic chain of narration.]
(Allaah is the Greatest. Allaah is the Greatest. Allaah is the Greatest and to Allaah belongs all praise. Allaah is the Greatest and the Most Sublime. Allaah is the Greatest to that which He has guided us to.)
Abdur-Razzaq transmits by the isnaad of Baihaqee in his book as Sunan al-Kubra (3/316)- with an authentic chain of narration - from Salmaan al-Khair (may Allaah Pleased with him): "Make takbeer of Allaah: Say: Allaahu-Akbar Allaahu-Akbar Allaahu-Akbar kabeera"
However many of the lay Muslims have opposed this dhikr that is established upon the pious predecessors (The Sahab & the Tabieen) by innovated dhikr and additions which have no basis at all. Thus Haafidh Ibn Hajr (may Allaah have mercy on him) said in Fath ul-Baaree (2/536): "indeed additions41 have been invented. on this day, which have no basis."
 Reported by Ibn Abee Shaibah in Musannaf and Mahaamlee in Kitaab Salaatul 'Eidain with an authentic chain of narration but it is mursal. Nevertheless it has (some) supporting narrations that strengthen it. Refer to Silsilatul Ahaadeeth as Saheehah (170). The takbeer begins from the time of the proceeding out to the musallaa until the prayer.