Eid Al Fitr
Allah says in the Qur’an , “(He wants that you) must complete the same number (of days), and that you must magnify Allah, (ie. To say Takbir- Allahu Akbar (Allah is the Most Great) for having guided you so that you may be grateful to Him.” (Qur’an, 2:185)

Eating to recognize that it is Eid and the end of Ramadhan

Anas reported :”The Prophet (peace be upon him) would not go out on the festival of breaking the fast (Eid al Fitr) until he had eaten an odd number of dates.” (Al Bukhari)
It is mustahab to eat before going out to emphasize that fact that it is forbidden to fast on the day and to demonstrate that the fast (of Ramadhan)has ended.

The Eid prayer
Umm “Atiyah reported: “We were ordered to go out with the single & menstruating women to the two Eids in order to witness the good & the supplications of the Muslims. The menstruating women should be separate from the others.” (Al Bukhari & Muslim)

Going to the prayer by one route & returning by another
Narrated Jabir bin Abdullah: “On the day of Eid the Prophet (peace be upon him) used to return (after offering the Eid prayer ) through a way different from that by which he went.” (Al Bukhari)

Fasting Shawwal
The Prophet (peace be upon him) said, “Whoever fasts Ramadhan then follows it with six days of Shawwal , it will be as if he fasted a lifetime.” (Muslim)

A women should complete her Ramadhan fasts first, then follow it with six days of Shawwal, so that the hadith with be applicable to her too, & she will gain the reward mentioned in it inshaAllah.