To quiet a neighbor's barking dog, start with talking to the neighbor. A friendly chat or a note may alert a pet owner who is unaware that barking is bothering you. However, quieting the dog may require getting help from the landlord, the police or even the courts.
Keep the discussion friendly, and take the lead in offering a solution, such as training or electronic collars. Making threats is never helpful, but if the neighbor is obnoxious about it, you may need to just go to the landlord, since rental agreements generally include what to do about noise complaints.
Lacking a common landlord, the next step may include recording and documenting the barking dates, times and durations. Contact the police and show your evidence. If all else fails, talk to an attorney about taking the issue to small claims court.