The first contact of /Starfleet? with the Borg occurs by interference from /Q with the mission of The Next Generation crew. Q transported the /Enterprise? into the [/Delta Quadrant]? just long enough to expose them to the Borg. The Enterprise was hopelessly overpowered, and Q brought them home after their confrontation. Q says something to the effect of "Now that they know about you, they will never stop until they find you."
They occur in that series several times, in the First Contact movie, and /Voyager even gets a (rescued) Borg crew member, [/Seven of Nine]?.
Borg changes over time The Borg have changed significantly over the years. Initially, they were a mysterious group of marauders that snatched entire starship crews or took over planets, and rather crudely and frighteningly assimilated the people by surgically altering them for joining the collective. As time went on however, this was replaced with the more efficient method of injecting nanites? into the individuals. The nanites would grow electrical input pathways to facilitate the later insertion of the Borg's notable brain uplink to the collective, holographic eye replacement and forearm control unit. This change continuity-wise could be explained that the nanites were a product of some race assimilated in the interim between movies.
At one point the Enterprise crew captured a single borg who, it seemed was detached from the collective with his whereabouts unknown. Seeing an opportunity to study their enemy, he is taken aboard the ship. Eventually, due to separation with the collective the Borg, known by the nickname "Hugh" to the crewmembers the Borg begins to develop an individual personality. Events lead to him eventually returning to the collective. He seemed to lose his individuality, but the introduction of his experiences into the collective had far reaching consequences. Some eventually broke away. they later joined with /Lor?, Data's prototype brother who helped them express their newfound emotions through hatred.
The purely collective nature of the Borg was later undermined in ''Star Trek: First Contact", which introduced the Borg Queen as the driving force behind the them. Continuity dictated no such person, as Borg always refer to themselves as "we", and Borg collective communications would have indicated the presence of a queen. The Queen refers to herself as "I", further complicating the matter.