1. A person who has missed any Rakaat and then joined the Jamaat should continue the Salaat with the Imaam to the end. Once the Imaam turns to say the second Salaam, the Masbooq should stand up and complete the missed number of Rakaats.
2. If the Masbooq has missed two Rakaats in Fajr, Dhuhr, Asr or Esha, he should complete both the Rakaats by reciting Surah Faatiha and another Surah in both the Rakaats.
3. If the three Rakaats were missed, the Masbooq should stand up and read Surah Faatiha and a Surah in the first Rakaat. After Sajdah (before standing for the second Rakaat he has to make Qa'adah - sit down - read Tashahhud and then stand for the second Rakaat. In the second Rakaat, he should recite Surah Faatiha and a Surah. Complete the second Rakaat without sitting for Tashahhud. In the third Rakaat, read only Surah Faatiha and complete the Salaat. Note: in the first Rakaat of the Masbooq (late comer) will recite Thanaa, Ta'awwudh, Tasmiyah, Surah Faatiha and a Surah.
4. The Masbooq should recite the complete Tashahhud (Attahiyyaat) only. A simple rule completing missed (whether you joined the Imaam in the third or fourth Rakaat), when you will stand up (after the Imaam make his second Salaam. Your first Rakaat which you will be making up for will be the first Rakaat you have missed with the Imaam. So first, offer those Rakaats in which there is Qiraat and then those which do not have Qiraat (Surah after Surah Faatiha). As for the calculation of the Rakaats, it should be done with that which was made with the Imaam. Then calculate in pairs accordingly.
If a person joins the salaat late, and forgets to get up to complete their missed salaat, what should the person do? If, after making salaam with the Imaam, the person looks to one side and then remembers his error and gets up, completes his salaat, with sajd-e-sahu, is his salaat valid?
Yes, his Salaat is valid. The condition in this instance is that his chest must not turn away from the Qiblah. If this happens, or if he talks, then his Salaat will break and he will have to repeat.
And Allah Ta'ala Knows Best,
Mufti Ebrahim Desai