The official scorer awards the win to the reliever who was "most effective" (assuming the lead is never given up). So a reliever could get 1 out and get the win if it was a really important out.

Otherwise it's pretty cut and dried, the pitcher of record when the winning team takes the lead for the last time. I was at an Orioles game once where Jesse Orosco came in up 3 runs with 2 outs in the middle innings. Walked 3, gave up a grand slam, then got the final out of the inning. The O's scored 2 to go back ahead in the bottom 1/2, another reliever came in to start the next inning and the O's won without giving up the lead again. Orosco was credited with the win because he was still the pitcher of record when the O's went ahead for good. I believe the scorer has discretion in a situation like that when the pitcher is deemed ineffective, but scorers have a lot of latitude in many of the rules and probably game Jesse the win because he was like 80years old at that point.