According to the comparative studies of all Indo-European languages, their phonetic, morphological, lexical and syntactical similarities and differences we can now judge about dialectal history within the community which was only about to brake up.
The difference of certain languages in forming the medium voice of verbs and the relative pronoun is considered to have marked the earliest division of tongues within the Proto-Indo-European language. According to it, the community was slowly breaking into two dialectal groups: one, including future Venetic, Illyrian, Anatolian, Tocharic, Italic and Celtic groups, used the relative pronoun kwis (which) or its derivatives; its medium voice markers were almost everywhere -r (Latin datur, Hittite kittari, Irish tuigear). The other group consisted of Indo-Iranian, Greek, Baltic, Slavic, Germanic, Armenian and Thraco-Phrygian languages, which took up yos as a relative pronoun, and endings -oi / -moi as medium voice markers.
We cannot geographically identify these two first major dialectal groups, but it is possible to say that this was the beginning of the new languages shaping process. Languages in both groups can prove their close connections by many lexical and morphological parallel forms.
3500 BC Anatolian branch moves apart
Several centuries after the Indo-European common language began to form dialects, the Anatolian subgroup is suddenly moves apart and start migrating to Asia Minor. This separation took part long before other branches started their own ways, so it is most interesting for the linguistics.
Really, the Anatolian branch preserved a great number of phonetic, morphological and syntactic traits which do not exist in any other Indo-European group. When Anatolians separated, Proto-Indo-European continued to develop new grammar features, and they exist everywhere but in Anatolian. For example, three genders known in all Indo-European tongues did not exist in Hittite and Luwian, there are no signs of feminine stems a, i, u of nouns there. The instrumental case plural masculine form in -oys can be traced everywhere except Anatolian languages. The same can be said about the demonstrative pronoun so, sa, to, unknown only in Anatolian.
As for phonetics, Anatolian was the only group which kept the laryngeal sound H both in the beginning and in the middle of the word. The laryngeal was soon lost in Proto-Indo-European, and subsequently in all later languages.
When the Anatolian language went away from the community, it continued its dialectal divisions. In about 3000 BC other groups began to migrate apart as well.
Map of Anatolian languages
More about Common Anatolian language
More about Hittite history
2500 BC Indo-Europeans appear in Europe
From the 22nd century BC, as archaeology supposes, people no longer migrate to Europe by huge waves. Though some invasions still took place, scientists stress that in this period significant movement of people back, from Europe to Anatolia can be observed. This makes us believe that in 2100 BC the most part of Europe was already inhabited by numerous Indo-European tribes, which could appear here in 2500 BC, or even a bit earlier.
It is known for sure that Indo-European migrants were moving from the east to the west, penetrating in Europe by two main routes: from Asia Minor via the Aegean Sea and southern Balkans (like Achaeans could go), and from the Steppes north to the Black Sea, then to northern Balkans and farther west along great rivers like the Danube. Archaeologists argue about the ethnic composition of certain cultures which can be traced in Europe at that time. Some think that the "pit" culture which spread from the Volga region to East Europe represented Indo-Europeans; some better studied cultures like "cord pottery", "sphere amphorae" and others can give more materials to study the problem.
In any case, no exact answer can be given about
the date of Indo-European coming to Europe, and what is given above
is just approximate.