I agree with a previous poster -- you need to pick the setting. But once you have it, my suggestion is to start with
who -- the
why follows naturally.
Is the murderer a local or an out-of-towner?
What age, gender, profession is the murderer?
Is the murderer married? Single? Divorced?
What sort of childhood did the murderer have?
What are two obvious strengths that the murderer has?
What's one strength that's inobvious?
What are two weaknesses that the murderer has?
What's one weakness that's inobvious?
What are three ways in which the murderer is just like your protagonist?
What's one way in which they're entirely different?
What are three things that the murderer could teach your protagonist?
Whom has the murderer murdered and why?
To answer these questions you need to answer similar questions for your protagonist. So here's a sample protag/antag pairing...
Susain Leclerc is a 38 year-old pastrychef and owner of Arthearth Patisserie in the fishing and tourist town of Bateman's Bay, where she and her husband recently moved. She's married to Peter, an 45 year-old insomniac workaholic accountant, which they joke works out well, since Susain works from 2am through 12pm at the bakery anyway. However Peter's age is beginning to catch up to him, and he's having chest-pains that he won't see anyone about. Susain has a step-daughter, Claire, who visits on alternate weekends.
Susain's patisserie does very well from street-trade in the high and shoulder seasons, but in the low tourist season it's a struggle. To keep the business ticking over across winter, Susain has been marketing to function-centres, conference-centres along the coast and has started to pick up winter wedding business. Susain's strengths are her cooking, her eye for detail, and her knowledge of Pomeranians, which her family has bred since she was a child. Her chief weaknesses are her hearing (a childhood viral infection damaged her cochlear), her excessive generosity with staff and customers (to the chagrine of her husband she's always loaning staff money, and giving customers excessive credit), and an utter loathing of frogs.
Bogden ("Bocky") van der Ness is a 28 year-old electrician recently moved to just outside the Bay area. He's taken a job with Sparks Electrical, run by Ron Sparks, which services a 30km region around Bateman's Bay -- mainly fitting out investment and retirement properties for the seachange crowd. The youngest of five, Bocky grew up with a violent, autocratic father and a strict Calvinist mother and something in Bocky didn't quite turn out right. He's smart with anything technical, has beautiful cornflower-blue eyes and a near-perfect memory for maps, but he's shy, stammers and has an obsession for red-haired women that stems from an adolescent experience in which he came across two of his teachers having an illicit affair. Bocky lives with his girlfriend Kelly, a local who has two children by a previous relationship.
In the last three years, Bocky's youthful fantasies have begun blossoming into psychopathic sexual predation. He has left two bodies hidden in seaside bushland in Wyee, 200mi north, where he used to live. However, his methods were sloppy then, and he fled south to avoid detection. Now that his methods are getting perfected he's taken to preying on solitary tourists around the Bay. He's not greedy, he tells himself -- he only takes one or two each High Season.
However, Bocky has made a mistake. A recent victim whom he thought was a lone surfer girl, was actually meeting her family down in the Bay for her wedding. Her disappearance has turned the Bay upside-down, and Bocky has gone to ground, with the girl's body safely hidden in bushland -- or so he hopes. But Bocky thinks he may have been seen by a jogger -- and now he needs to silence that person too.
Susain's connection? She'd made the wedding-cake -- a six-layer profiterole affair that had taken her days.
How Bocky and Susain are alike: they're both hard-working with a good eye for detail; both are relative newcomers to the Bay, without the extensive social networks that locals have.
How they're opposites: Susain is open and generous; Bocky is selfish and private.
What Bocky could teach Susain: Don't give anyone more than you can afford to lose; it's the people closest to you who can hurt you the most.
Hope that helps.