And your understanding is correct. but if they are in sajdah/sujood (prostation) then you have to go in prostation and say Subhana Rabbiyal ala.

When you arrive late, and the prayer has already begun, you go to the last row and have your intention that your praying for example 4 rakat fardh of Asr salah following the Imam, then you say Allahu Akbar. and join the prayer where they are. So if they are in Ruku, then you go in ruku too.

Suppose you missed one rakat and you joined them in the second then when the Imam makes the first salam, at the end of the prayer, and when he goes to the second one, you stand up and complete your first rakah, by reciting Surah Fatiha and a Surah and then going to ruku, sajdah(prostation) then you go in the sitting position, recite Attahiyatu lillahi, then allahumma salli, basically finish it as the normal salah.

For a better understanding of this please read the following and possible save it or buy it from an islamic bookstore -

Few keywords to know before seeing the actual link: Muqtadi means the person who is praying behind the imam.

Also this book is called Bahishti Zewar (Heavenly ornaments)

And for your question, please refer to

Check #9-12. That is for your question.
http://www.jamiaashrafia.org/bahishti_zwear/bahishti_zwear_title.php?title=Virtues%20Of%20Salaah%20With%20Jamaat
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I am Turkish Hanafi. We make Takbeer/Shahada while standing, then go to position Imam is in, but if they are in ruku, make sure you do one sajdah first (face touches ground). As for making it up, you can make the rekats you missed, including the "imperfect" one. For instance in a four rekat set, if you missed the first rekat completely and joined in the second one, make up the first two.

Check with your Imam.
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and when the jamat is over do not say " asalam u alekum warehmatulah" but when the imam says that stand up and finish the rest of your rakats that you missed with the jammat.

and that is how you do it.

anyways salam!!!
PIECES!!!
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Yes, if the imam is in whatever position is in, you make the takbeer (raising the hands and saying Allahu Akbar) for salaat and go into whatever position the imam is in. You say whatever position you are in. (i.e. "Subhana Rabbiyayil Azeem")

As far as stating the intention, you just say it in your mind. There’s no point in saying it out loud, and Allaah already knows you’re joining in late. Remember when you arrive at the Masjid, not to run towards the salaat. It’s sunnah to take your time and walk. You should not rush and run, for Allaah wants for you ease and to be at ease.

And remember as far as making up salaat, once the imam does ruku, not sujud, you already missed that rakat, and need to get back up before finishing the salaat. (From my understanding. May Allaah forgive me if I’m wrong.)
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Muslim

A star for you.

salam alaikum
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