The very existence of a group that we might distinguish as Indo-Europeans, their region of origin, the extent to which they moved en masse, and the timing of their migrations are topics that remain in scholarly contention.
Since the concept of Indo-Europeans is a modern one, we need to work backwards from the present. We know that there are grammatical and etymological similarities between the languages that currently dominate in most of Europe, the Americas, the Indian sub-continent, and through English, the Internet. From this we have inferred that some form of “Proto Indo-European” was spoken around 4,000-5,000 BCE. Where was it spoken? There appear to be two main candidates: the steppe lands of Western Iberia and the plains west of the Caspian Sea. Either through mass migration or through selective conquest (or through a more passive imitation model) aspects of Indo-European culture including language, religion and some technology became dominant over the next 3,000 years. From either homeland there appears to have been a double movement: westward into Europe and all the way to the Atlantic, and south-eastward into India.
Whatever the exact story, we can consider Indo-European culture, broadly defined, as one of the first cases of globalization as it created links between different regions and peoples and also created a common form of communication through which exchange could take place.