There are only 2 ways in which you can attack other players (Klingons or Feds).
1) Ker'rat, in the Eta Eridani Sector Block. In there is a mission where you must decrypt Borg tranmissions. However, both Klingons and Feds are fighting over the same goals so you can attack the other faction.
2) PvP queues: You can choose to engage in Fed v Klingon, Fed v Fed, or Klingon v Klingon. Once enough people volunteer, you'll get a message saying that a match is ready to start. If enough people accept, your match will start and you can attack the others that are not on your team.