Questions on completing a jama'ah salah that has already started

Salam, Okay so I've had this question for a while and I don't know it's kind of funny to me that I still don't know how, but I don't know how one is supposed to make up the raka'as in the prayer that you miss.

Like, say that everyone is on the third raka'a, so you do what they are doing and do you say "assalamalakum.." in the end and then get back up and make up raka'a 1 and 2 ? In other words, Are you supposed to continue what the jama'ah is doing and end the salah and get back up to do the other raka'as you missed?

Also, when is the best time to get into a prayer, asap? Or when they're standing? In sujood?

JAK