Step by Step Method of Praying Eid ul Fitr:

1. The prayer would be started with Takbeer e Tehreema (اللہ اکبر) . After saying اللہ اکبر, you would place your hands in position. Then, the extra Takbiraat would be said. It is upto you to do Rafa Yadain (raising hands till your ear lobes while saying اللہ اکبر ) or keep your hands on your chest in position while saying the extra Takbiraat. 
2. After Takbeer e Tehreema, there is no dhikr or dua in between the extra Takbiraat.
3. The Most common number of extra Takbiraat is seven, i.e, seven extra Takbiraat other than the essential Takbeer e Tehreema (Takbeer e Tehreema + 7 more Takbiraat). But you can also make it seven including Takbeer e Tehreema (Takbeer e Tehreema + 6 more Takbiraat). There is a slight difference of opinion regarding the number of extra Takbiraat, but both opinions are acceptable.

Evidence:

Prophet of Allah صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم  while offering the Eid Prayer said seven Takbiraat before recitation  قراؑت in the first Rakat and five Takbiraat before recitation in the second Rakat.

Tirmidhi: 536

After seven Takbiraat in the first Rakat, recite Surah Al-Fatiha, followed by recitation of Surah Al-Qamar (اقترابت الساعة و انشق القمر) in the first Rakat and Surah Qaf (ق) in the second Rakat. Or, Surah  Al- A’la  ( سبح اسم ربک اعلیٰ)  in the first Rakat followed by Surah Al-Ghashiya (ھل اتاک حدیث الغاشیة)  

Recitation of these surahs is Sunnah, but you can recite any surah.

Evidence:

Prophet of Allah صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم   used to recite ( سبح اسم ربک اعلیٰ)   and  (ھل اتاک حدیث الغاشیة)  in the Jumuah and Eid Prayers. Sometimes both would be on the same day, even then he used to recite both these surahs (both times).

Tirmidhi:533

Evidence 2:

Omer bin Khattab asked Abu Waqid al-Laithi what the Messenger of Allah  ‌صلی ‌اللہ ‌علیہ ‌وسلم ‌ used to recite on Eid-ul-Adha and Eid-ul-Fitr. He said: He used to recite in them: (Surah Qaf ) ق والقرآن المجید, (Surah Al-Qamar )اقترابت الساعة و انشق القمر

Sahih Muslim:2059

After completing the recitation قراؑت , go into the Ruku after saying اللہ اکبر, and then complete both sajood. 

After sajood, when you stand up to start the second Rakat, you would say five Takbiraat (Saying اللہ اکبر five times). Afterwards, Al-Fatiha and then any other surah would be recited, and then the rest of the prayer would be offered as usual. In this way, the Eid Prayer would come to an end.

Eid Khutbah:

Usually, next comes the Eid Khutbah. It should be noted that Friday Khutbah is different from Eid Khutbah. Friday Khutbah is amongst the obligatory (essentials) while the Eid Khutbah is Mustahib (good to have).

Evidence:

Abdullah bin As-Sa'ib narrated that: The Prophet of Allah  صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم offered the Eid prayer and said: Whoever would like to leave, let him leave, and whoever would like to stay for the Khutbah, let him stay.

An-Nisai:1572

Woman/ Young Child as Imam:

In the houses where no men are around at the time of Eid, a woman would lead the Eid Prayer as usual, but she would not stand in the front as the male Imam does; Instead, she would stand in the middle of the first Saf. A woman would lead the Eid Prayer, but the Eid Prayer MUST be offered, even in the absence of any men.

Another scenario is that the house does have male members, but they have not reached adulthood. However, the child does know how to perform wudu, can offer salah and has memorised some part of Quran, then this child would lead the Eid Prayer and women would follow him.

Evidence:

In the times of Prophet of Allah  صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم  , a six year old child used to lead the entire village in Prayer. This is evidence that a male child that has yet to reach adulthood can lead Prayer.

Sahih Bukhari:4302

Remember:

• If due to current circumstances, you are going to offer Eid Prayers at home, then according to the majority of Scholars, there would not be any Eid Khutbah. It is because to deliver the Khutbah, you need to be knowledgeable about the Quran and Sunnah. Unfortunately, about 90% of the Muslims do not fit the criteria. If they do not even know how to offer Eid Prayer, how can they deliver the Eid Khutbah?
• Although Imam Bukahri has provided evidences for Eid Prayer in his book, but he has not provided any evidences for Eid khutbah.
• Anas bin Malik instructed his slave (who was living in a far away place with his family) to offer Eid Prayer, but did not instruct him to deliver Eid Khutbah/ Sermon.
• The Companions of the Prophet instructed to offer Eid Prayer by one’s self if one has missed it with congregation, yet they did not mention the Eid Khutbah.

Conclusion:

The Eid Prayer that would be offered in homes would not include Eid Khutbah.