I doubt that anyone can truly answer your question about the exact origins of the Indo-Europeans simply because there are no solid records.
One set of clues about the homeland of this large group of prehistoric people comes from the language that they probably spoke, called Proto-Indo-European (or PIE). PIE is a theoretical and reconstructed language; like the people who may have spoken it, it has no clear records. The language has been reconstructed through extensive comparisons of recorded languages (ranging from Sanskit to Latin, but hardly stopping there) that have clear similarities in grammar and vocabulary. As these daughter languages tend to have very similar native words for "cow," "snow," "wolf" and no similar native words for "beach" and "ocean," for example, it stands to reason that the PIE people used animal husbandry and agriculture, lived somewhere fairly cold, and did not live directly on a large body of water. In what's called the "Urheimat" (or "ancient homeland") theory, the PIE homeland is located in southwestern Russia and dated back to around 5,000 BC.
Whereever the PIE people came from, they sure got around for a prehistoric people. They spread eastward as far as India and westward well into what is now Western Europe (hence the name Indo-European). Early theories about this group presented them as militaristic, but recent theories sometimes present them as more peaceful in their expansion.
Indo-European is a term used for people who are supposed to be common ancestors of ancient Greek and ancient Aryan people. The Indo-European people must have lives several thousands of years ago (at least before 2000 B.C.) in the southeastern part of Europe in the area north of Black Sea. One group of Indo-Europeans migrated westward up to Greece. Another group who later developed as Aryans, migrated southward into northern India. The Indo-Europeans also migrated in other regions of Europe and Middle East.
Various languages that have been derived primarily from the language of the Indo-Europeans are collectively called Indo-European languages.