"Indo-European" is the name of a family of languages that includes the Celtic, Germanic, Italic, Baltic, Slavic, Albanian, Hellenic, Armenian, and Indo-Iranian branches, as well as a number of smaller, dead branches such as Illyrian, Venetic, and Anatolian (OK, the last is not too small, but it is dead). If you are reading this, you can read at least one Indo-European language, since English is part of the Germanic branch.
People who speak an Indo-European language as their primary tongue can loosely be described as "Indo-European." Note that it is a language indicator, not a racial one. You are not an Indo-European by genes. How many people whose ancestors came from Africa or Asia have English as their primary language? They are Indo-Europeans too, no matter what the color of their skin.
This can not be stressed enough. The idea that "Indo-European" is some sort of racial term has been the source of everything from confusion to downright evil. The Nazi racial theories, with the concomitant Holocaust, was a result of such a belief. ("Aryan" was sometimes used to mean "Indo-European," although it more properly refers to the Indo-Iranians. Needless to say that, like the swastika, its perverted use by the Nazis has limited its modern use greatly.)
However, since language is a carrier of culture, it can roughly be said that there is an Indo-European culture. More precisely, just as the Indo-European languages are related, there are cultures that are also related that may be called "Indo-European." This is similar to the way that "Celtic," which is a linguistic term, has been applied to a certain group of related cultures.
It is clear that when you have a family you have an ancestor. The ancestor of the Indo-European languages is Proto-Indo-European (PIE). This language no longer exists, and did not exist in any time during which there was writing (at least not in the area where people speaking it existed), so all of what we know about the language has been reconstructed. The descendant languages have been compared, rules for sound changes observed, grammatical structures taken into consideration, and from all of that has emerged a picture of a language -- of Proto-Indo-European. There are still arguments over a number of the particulars (don't even bother to ask me about laryngeals, how many there were, and how they were pronounced; the very arguments are so far over my head that I am just waiting for the dust to settle so I can use the information), but there is also a surprising amount of agreement, especially on many items in the basic vocabulary.
For instance take the following (and for your first lesson in linguistic representation, you can learn that an asterisk before a word means that it has been reconstructed rather than being seen written down or heard spoken):
*oino, *dwo, *trei, *kʷetwor, *penkʷe, *ses, *septṃ, *okto, *newṃ, *dekṃ.
Or try this series:
*ptḗr, *máter, *bhráter, *swesor, *sunnus, *dhughter.
Congratulations; you can read Proto-Indo-European.
Of course, not all of PIE is that recognizable; a PIE word may not have survived into Germanic or been borrowed into English. But a lot of them have been, and PIE as a result has the aura of an old friend.
Now let us return to the question of who the Proto-Indo-Europeans were. Just as "Indo-European" can carry a cultural meaning, so can "Proto-Indo-European." The Proto-Indo-Europeans were those who spoke Proto-Indo-European. We do not know what race they were, although they were most likely predominately Caucasian. However, that does not even matter; what matters is their language and their culture.
Just as we can reconstruct their language by comparing their descendant languages, we can reconstruct their culture by comparing their descendant cultures. Elements of the cultures are compared, patterns noted, and shared elements postulated as inherited. From that sort of work we can figure out what culture the PIEs had.
On the pages about the deities and the rituals, I give many of my sources. They are not all of the ones I used; there are so many it was hard to put them all in when I wrote the book on which these pages are based. However, I am going through all my notes, papers, and books, and putting the sources in here. This is an on-going project, so sometimes I will be giving only one or a few sources on something for which I have many more. This will change as time goes by; in the meantime, if you want to know more about my sources, send me an e-mail and I'll see what I can do.
How long ago did the Proto-Indo-Europeans live ?
Where did the Proto-Indo-Europeans live ?
What kind of culture did the Proto-Indo-Europeans have ?
What was the Proto-Indo-European religion like ?
Proto-Indo-European Language Information
Putting it All Together in Proto-Indo-European
Speculations on the Xártus