This is a really tough one, and the interpretation has made monkeys out of a lot of us who think that we know a lot. Therefore, for what is to follow, you owe me a banana.
Our languages, in certain cases, were one. Not all languages. Arabic, and Hebrew, for instance, are very closely related, and they do not relate to English,German, Dutch, French, Italian, Spanish and the rest of that. Or to Iranian or any of the north indian languages, or, separately, to the Dravidian languages, Tamil, Telugu, Kannada or Malayalam. Or to Chinese. Or to Japanese. Or to the languages spoken in south Africa.
There are different 'language groups' used by scholars to group languages that they consider similar. These groups are highly controversial. Linguists do not agree completely on which language goes into which group, or how much a group should cover. There are languages which do not fall into any group at all, and have no resemblance to any other. One, Burashaski, spoken in Pakistan has no known connections. Others, Finnish and Magyar, spoken by the Hungarians, are close to each other, but to no other language. Perhaps one of the stablest and most robust groups, because languages within them have remarkable resemblances, is the Indo-European group of languages. In India and in Pakistan, this includes Punjabi, Sindhi, Pushto; Hindi, Marathi, Gujarati - in fact, most of the languages well known in north India.
That was the easy part. Now comes the difficult part.
People speaking the same language are not necessarily related to one another, or descended from common ancestors. They just happen to be speaking the same language.
We do not know for certain who brought the first of the Indo-European languages into India. This was Indo-Aryan, known more commonly as Vedic Sanskrit. it might have been an individual, or a single family, or a group of families, or a tribe, or a group of tribes, or a whole people, including all its tribes. At the moment, by reading the Vedas carefully and analyzing its contents, it seems that there may have been a group of tribes, who seem to have had connections with tribes that they left behind on the other side of the Hindu Kush, and kept up these connections for several hundreds of years after they first separated.
What happened to those who came into India? They vanished. They were relatively so small in numbers compared to those already staying there that in a few centuries, they mingled completely with the original inhabitants. Now, to make out who came from where, it needs blood analysis of a very sophisticated type to figure things out.
Rather than putting things in place right down to the last comma, it seems preferable to let people draw their own conclusions.