140--S- Joins prayer late

After reading Subhanaka, he recites audhu basmala, al-Fatiha and some verses from the Quran.

How to Join Salat al-Jamaat

Make the niyyat (intention) that you are praying behind and following the Imam who is leading the Salat. It is not necessary to know his name, however, you should know that you are following that particular Imam.

Your Salat will not be counted as Salat al-Jamaat if you do not make the intention of following the Imam, this is important.

The follower must say the Takbiratul Ihram after the Imam, so as to maintain his Salat al Jamaat.

Listen to the Imam

In  the first two Rak'at, the Imam will read Surah al-Fatiha and one more complete Surah of the Holy Qur' an.

If you are praying the Salat of Fajr, Maghrib and 'Isha, then the Imam will be reciting these Surahs out loud, thus, you should keep silent, and listen to his recitation.

In the Salat of Zuhr and ‘Asr, the Imam will be reciting in a quiet whisper and you will not recite anything out loud, however, it is Mustahab that you recite any Dhikr of Allah (swt).

Recite Everything Else in Jamaat

Apart from the two Surahs  which the Imam alone will recite, you must independently recite all the other things in the Salat.

You must pray the Dhikr of Ruku, Sujud, Tashahhud, Salam, and all the Takbirs, etc.

So remember, that a Ma'mum is exempted from reading only the two Surahs in the first two Rak'at.

Follow the Imam

The Ma’mum must say theTakbiratul Ihram (the first) after the Imam has said it.

If you say it simultaneously with the Imam or before, then there will be no Jamaat for you.

Then, in every act, follow the Imam. When the Imam goes into Ruku ' Sujud, or rises, do it either with him or after him; but do not precede him. This is important as far as the acts are concerned.

However, in the case of the recitations like the Dhikr in Ruku', Sujud, Qunut, etc., you may precede the Imam, even the Salam to complete the Salat.

If you forgetfully rise from Ruku' or Sujud before the imam, you must return to the Ruku ' or Sajdah position (as the case may be) provided that the Imam is still in that position.

http://al-rida.net/index.php/islam/faqs/prayer-faq/tags/6-prayer

Scenario-1: who joins the imam in the second rakat of the morning prayer:

A person who joins the imam in the second rakat of the morning prayer recites takbir and keeps silent. He recites tahiyyat in the last sitting and stands up when the imam gives salutation; (1)

 he starts performing the rakat that he has missed. After reading Subhanaka, he recites audhu basmala, al-Fatiha and some verses from the Quran.  (2)

After the ruku and sajdahs, he sits and reads at-tahiyyat, salawat and rabbana atina; then he gives salutations.

Scenario-2:  who joins the imam in the 3rd rakat in evening prayer?

If Masbuq joins the imam in the last rakat of the evening prayer, he reads Subhanaka and performs that rakat with the imam and sits in the tashahhud; then, he stands up and  (1)

recites audhu basmala, al-Fatiha and some verses from the Quran. (2)

He sits after the ruku and sajdahs and reads only at-tahiyyat.

Then he says Allahu Akbar and stands up. He reads basmala, al-Fatiha and some  verses from the Quran and performs the ruku and sajdahs; (3)

 then he performs the final sitting and gives salutations, finishing the prayer. Thus, he performs tashahhud three times. However, if Masbuq forgets and does not sit after the second rakat, sajdah sahw is not necessary for him because that rakat is regarded as his first rakat. 

Scenario-3:  joins the imam in the fourth rakat of a four-rakat prayer:

If Masbuq joins the imam in the fourth rakat of a four-rakat prayer, he stands up after sitting for tashahhud with the imam. (1)

He reads audhu basmala, al-Fatiha and some verses from the Quran. (2)

 He sits after the ruku and sajdahs and reads only at-tahiyyat.

Then he stands up and reads basmala, al-Fatiha and some verses from the Quran and performs the ruku and sajdahs. (3)

He stands up without sitting and performs one more rakat reading only basmala and al-Fatiha  (4)

and sits. He reads reads at-tahiyyat, salawat and rabbana atina; then he gives salutations. 

Scenario-4:  joins the imam in the third rakat of a four-rakat prayer:

If Masbuq joins the imam in the third rakat of a four-rakat prayer, he reads only at-tahiyyat in the last sitting and stands up. (1,2)

 He reads subhanaka, audhu basmala, al-Fatiha and some verses from the Quran   and performs the ruku and sajdahs;   (3)

then, he stands up, reads basmala, al-Fatiha and some verses from the Quran and performs the ruku and sajdahs;  (4)

He sits and reads at-tahiyyat, salawat and rabbana atina; then he gives salutations, finishing his prayer. 

Scenario-5:  joins the imam in the second rakat of a four-rakat prayer:

If Masbuq joins the imam in the second rakat of a four-rakat prayer, it means he has performed three rakats with the imam; after tasahhud, he stands up and reads (1,2,3)

 subhanaka, audhu basmala, al-Fatiha and some verses from the Quran and performs the ruku and sajdahs. (4)

Then he performs the last tashahhud and completes his prayer with salutation. 

Scenario-6:  who joins the imam when he is in the ruku:

A person who joins the imam when he is in the ruku, he is regarded to have caught up with that rakat. However, if a person who joins the imam when he is in sajdah, he is regarded to have missed that rakat. Therefore, he needs to complete that rakat in accordance with the descriptions above. 

A person who joins the imam in the 3^rd rakat, performs two more rakats when he stands up by reading al-Fatiha, and some verses from the Quran.

http://www.questionsonislam.com/question/when-someone-joins-congregational-prayer-progress-what-should-heshe-do-and-recite