If a man enters the masjid while the imam (leader of prayer) is praying.
Should he join the imam immediately in whatever position he is in and
start praying, or should he wait to find out whether the imam is going to
sit or stand?

The correct answer is the one to which the evidence points. And
that is that he should enter with the imam no matter what part of prayer
the imam is in—sujood (prostration), qiyaam (standing),
rukuu’ (bowing) or qu’ood (sitting). The evidence is the hadith
of Abi Huraira (may Allah be pleased with him), in which he said, “The
Messenger of Allah (peace be upon him) said, ‘If
you come to prayer and we are prostrating, then you should prostrate [but] don’t
count it, and whoever catches a raka’a, then he has caught the
salaat’.”1
And Mu’ath said that [the Prophet] (peace
be upon him) has said “If one of you comes to prayer and the Imam is in
a certain position, then do as the Imam is doing”.2
Also, the general meaning of his saying (peace be upon him), applies: “What
you catch up with, pray.”

From the book What Should You Do in
the Following Situations… ?

1 Sunan Abu Dawood 893
and Sahih Sunan Abu Dawood 792.
2 Sunan Al-Tirmidhi 591
and Sahih Sunan Al-Tirmidhi 484..