Question Summary:
How does one make up one or more missed rakats in congregation?

Question Detail:

Can you please explain to me how one must read one or missed rakats in jamaat?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
A person who missed the 1^st rakah of a congregational prayer and joined only after the Imam had stood up from ruku is known as a masbuq. This is regardless of whether he missed one or more rakahs.
The masbuq will pray whatever rakahs he gets with the Imam but will not make salam with the Imam. Rather, he will wait to ascertain that the Imam is finishing the salah and not making sajdah-sahw. As soon as he is sure of that (i.e the Imam begins the 2^nd salam)  the masbuq will stand up and recite the thana', the tawawwudh, the tasmiyah and make up his missed rakahs. [i] [ii]
In terms of recitation, the masbuq will look only at the rakahs he is praying by himself (i.e. he will not take into account the rakahs he got with the Imam). So he will recite another surah in addition to Surah Fatiha if he missed 1 or 2 rakahs.
If he has missed 3 or 4 rakahs, he will still recite Surah Fatiha and another surah in the first 2 rakahs he prays on his own, but only recite Surah Fatiha in the remaining missed rakahs.
For the sitting in tashahhud, the masbuq will look at the total number of rakahs (those he prayed with the Imam and those he prayed by himself). [iii]
For example, if he got one rakah with the Imam, then the masbuq will stand up and pray a rakah on his own. He will then sit in tashahhud in this 2^nd rakah, because the total number of rakahs he prayed is two (one with the Imam and one by himself). This is because the tashahhud comes after every 2 rakahs, with the exception of Maghrib where it is in the 2^nd and 3^rd rakah.
And Allah Ta’āla Knows Best
Sohail ibn Arif,
Student Darul Iftaa
Chicago, USA
Checked and Approved by,
Mufti Ebrahim Desai.