Takbir outside the prayer is of two types:
a) at-Takbir al-Mutlaq (unrestricted takbir) and,
b) at-Takbir al-Muqayyad (restricted takbir)
• UNRESTRICTED TAKBIR: It is recommended to say the Takbir starting from nights before both Eids (meaning from Maghrib of the night before and also from the beginning of the 10th of Dhi-l Hijjah) all the way until the Imam finishes the Khutbah.
Unrestricted means it isn’t restricted to only saying Takbir after congregation prayers, rather you do it when you are at home or in the car or on the way to the mosque etc.
Should we do Takbir whilst the Imam is delivering the ‘Eid Khutbah? – Yes, but only when the Imam himself does it and not on our own.
• RESTRICTED TAKBIR – This is when we do the Takbirat after the congregational prayers, but this is restricted to ‘Eidu-l Adha and is not done on ‘Eidu-l Fitr.
This means that there is no Takbir after congregational prayers on the night before ‘Eidu-l Fitr nor on the day of ‘Eidu-l Fitr. Instead, one does Takbir without restricting it to the congregational prayers.
How to do the Takbirat:
Allahu Akbar Allahu Akbar La Ilaha Illa-l lahu Wa-llahu Akbar Allahu Akbar Wa Lillahi-l Hamd
اللهُ أكبرُ اللهُ أكبر لا إله إلا اللهُ وَاللهُ أكبرُ اللهُ أكبر وَلِله الْحَمْد
This answer was collected from The Hanbali Madhhab website. The answers to the questions are given by Imam Zahed Fattah in accordance to the Hanbali School of Jurisprudence.