Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The correct way of performing the first two Raka'hs of al-Fajr, al-Maghrib and al-Isha prayers behind the Imam is as follows:
1) To raise one's two hands and say Allah-u-Akbar after the Imam.
2) To recite al-Istiftaah supplication if it is possible before the Imam starts reciting al-Fatiha in aloud voice; otherwise, one should listen to the Imam since it is Sunnah (al-Istiftaah) while listening to the Imam is a must.
3) To recite al-Fatiha when the Imam completes its recitation even though he starts recitation of the additional portion after al-Fatiha, since - according the most correct opinion - it is obligatory to recite it.
4) To listen to the Imam after the completion of al-Fatiha.
5) To follow the Imam's movements while making Ruku' and to say: Subhana Rabiyal 'Azeem.
6) To return to the erect position after the Imam and to say: Rabbana Walaka-al-Hamd after the Imam's saying Sami'allahu Liman Hamdah.
7) To follow the Imam while making the Takbir of Sujud and to say in Sujud: Subhana Rabiyal A'ala.
8) To follow the Imam in the sitting position and pray saying: Rabbi Ighfirli.
9) To reprostrate himself after the Imam and make the supplication of Sujud as before.
10) To follow the Imam when he says Allah-u-Akbar to start the second Rak'ah, and to do as done in the first Rak'ah.
As for the first 2 Raka'hs of al-Zuhr and al-Asr, one has to recite al-Fatiha prayer in secret, and then, any portion of the Qur'an.
As for the 3rd Raka'h of al-Maghrib and the 3rd and fourth Rak'ah of al-Isha, one has to do as done in the 2nd Rak'ah and should recite only the Surah al-Fatiha in secret and without reciting any portion of Qur'an as stated by the majority of Muslim scholars.
Allah knows best.