After driving through the night in their pickup truck holding their life's belongings, divorced mother Emma Moriarty (Sally Field) and her son Jake (Corey Haim) arrive at their new home in Eunice, AZ. The property is a run-down ranch fixer-upper, so they resignedly set to work cleaning and repairing. Emma has grown up working hard and is handy with hardware, and they work well together to get the place in shape. She goes into town to install flyers under car windshields to advertise her services as a horse boarder and trainer. When she comes to the corner drug store on the main road, she stops to admire the beautiful vintage car parked there before starting to add her flyer; she is interrupted by the store and car owner, a widower named Murphy Jones (James Garner), who says her paper will cover the stickers championing his various causes. She asks if she can display it in the store window. After reading the sheet, he agrees. She sits at the old-fashioned soda fountain to learn about her new neighborhood. She tells Murphy she has moved there from Modesto, CA, this time; he tells her the town is progressive enough to have a cross-dresser, but she should go elsewhere to raise public consciousness.
Jake starts at his new school (he notes that they have no computers), and Emma spends a lot of time alone waiting for business to perk up (or actually start), and she keeps Jake up late playing rounds of cards. One evening they go to town together and spot Murphy playing fiddle at the weekly dance. He stops to talk to them during a break and tells them he shares the stage with other local town officials. The available women outnumber him, so he is a busy widower. He has an ongoing feud with the town over parking his classic car in front of the store and not feeding the parking meter. Vandals have been a problem, so he wants to keep the car close where he can watch it. While Emma is in the town hall to get a license for her business, she overhears him while he pays his fines (he has 22 outstanding tickets at $10 per day to pay off to avoid getting arrested). When Emma says one can't fight city hall, Murphy replies that one can wrestle them. He proposes that the town plant a tree, which he will pay for, in place of the meter, and the officials give in; soon the public works department removes the meter and installs Murphy's tree.
Things become tough for Emma, as the bank can't provide her a loan while she has no collateral (though she argues she is her own collateral) and is paying off the truck. She stops by Murphy's pharmacy to see if she can get a loan. He shows her that he is carrying several townspeople on his books to help keep them on their feet, and since he hardly knows her she would be at the bottom of the list. Back at home she tells Jake they have to be frugal as money is running out. The boy goes into town to find a job, and Murphy offers him a dishwasher job after school, then takes him for a ride in the 1927 car, which he has maintained showroom new. On the way he picks up the town's oldest resident, Amos Abbott (Charles Lane), who is walking down the side of the road. He tells them he has found love at age 89 with an elderly widow. The cantankerous senior asks Murphy to let him off before getting to his destination, however, as he complains that Murphy drives too fast at the car's top speed of 30 mph.
Emma finds Murphy one day at a horse auction. She has already strolled the grounds and checked out some of the animals up for bid. She sits with him and points out the problems with each horse that comes up on the block, until a healthy one appears for Murphy to bid on; he ultimately buys the horse and boards it at Emma's, where he comes and watches her train it, and he starts to admire her character.
On the way home one afternoon, Emma is tailgated by a rambunctious young driver who causes her to swerve off the road and hit her head. He stops to check on her, but she faints when he says he has no insurance. Murphy visits her in the hospital where she is crying at the thought of the expenses of staying there. He has some good news for her: he put the word out and some folks from town have put up their horses at her place. She breaks down and sobs that she worries she is raising her son all wrong, then blurts out that she is 33 years old and living like a nun. He cajoles her into taking a walk down the hospital hallway with him while he addresses her concerns; he has observed that her son is a fine young man, and to avoid living like a nun she should say yes next time she is asked. Before leaving he wryly notes that her hospital gown was open in the back the whole time they were talking.
Emma finally gets home to find a new problem waiting on her porch: her ex-husband Bobby Jack (Brian Kerwin) has found her and claims he has changed his spots and is a reformed man. Emma worries about his past habits, including spending money they didn't have (but helping himself to hers), but he is out of work and she can't bring herself to put him out, so they settle into an awkward routine. Of the three, Jake is happiest, enjoying having his dad back in his life.
Murphy meets Bobby Jack in the stable, and they civilly maintain an aloof tolerance. Emma sets her ex to work with her on taking care of the horses. When the house's only toilet stops up (due to a flushed cigar butt), Murphy comes to the rescue as Bobby Jack is inept at plumbing. Making small talk, Murphy notes that he can also sew as he was an only child and his mother was a widow who taught him how to follow a pattern. He ignores Bobby Jack's comments on that information. Emma invites Murphy to stay for dinner, and soon it becomes a ritual, with Murphy spending more evenings at the house.
During a game of cards, Murphy excuses himself and Bobby Jack. On the porch Murphy calls him out for dealing off the bottom of the deck when they're only playing using matchsticks for money. He warns not to do it again, especially in front of Jake. When Bobby wonders what they'll tell Emma and Jake about why they stepped out, Murphy replies, "Tell them we had a pissing contest and you won."
Low on funds, Bobby Jack helps himself to Emma's wallet while she is sleeping, and the next day uses the money to buy Jake a hat to impress his son. Murphy is in the shop, buying his signature shirt (which the clerk says keeps him out of fashion, but Murphy likes the style), and he stops to say hello. The four of them then go together to the movies and catch the latest slasher movie installment. Murphy is the first to bow out of the gory movie, and Jake soon joins him outside. Jake tells Murphy he saw his dad cheating at cards, and Murphy tells the boy it was probably a good thing that he noticed, and he can decide whether or not to take after Bobby Jack. Emma is next to arrive, repulsed at the "human hamburger" onscreen, when she notices some activity nearby; Murphy says there is a weekly bingo game and they join in.
In the ladies' restroom between games, a local woman tells Emma that Murphy's wife died suddenly, never having been sick a day in her life. Murphy was an emotional wreck and reclusive for years afterward. At the next round of bingo, Emma wins the biggest jackpot of the night: $200. Bobby Jack uses the bingo funds behind Emma's back to buy beer for a big party to which he invites the entire town. Murphy and Emma wind up doing dish duty while the others have fun. Emma asks Murphy how old he is and Murphy creatively dodges the question. When he takes out a load of trash and runs into Bobby Jack, who accuses him of "banging" Emma, Murphy won't be baited into an argument. Some time later, at a benefit dance, Emma finds herself with both men trying to usurp her time on the dance floor, cutting in on each other before either can get a dance with her; she finally stops, joins their hands and tells them to dance with each other as she has had enough, and they gamely dance their way off the floor to the other folks' amusement.
One evening Emma invites Murphy to dinner, but he doesn't seem interested, so finally she confesses that Jake wanted to see him; when he enters the house he finds they have arranged a surprise birthday party for him. He thanks them for tolerating him in his darker moments, grateful for their support. Emma takes him aside and asks him how many candles they need on the birthday cake, and he tells her to set thing on fire.
While Emma and Bobby Jack are putting hay in a stall, he makes a move to kiss her, but suddenly she is overcome with sneezing and ruins the mood. She realizes that it's time to make up her mind; she picks up Jake from school and tells him that she will be putting his dad out because they can't continue to live together as if they are still married. She apologizes to him for the realities he has had to face, but he asks to be dropped off and wants to walk home the rest of the way.
When Emma gets home, a strange truck is parked there, and in the house is a young woman named Wanda (Anna Levine) with twin baby boys Linus and Larry; they're Bobby Jack's children. Emma tells her to consider learning typing or a skill in case she needs it, but Wanda just wants to stay home with the children. When Jake arrives home, she sits the twins in his lap and introduces her son to his new brothers. Emma talks to Bobby Jack on the porch and tells him that he has to start being responsible. Though he balks at first, he realizes he has used up his time as a free spirit and leaves for good with Wanda and the kids.
Confused and lost, Emma goes into town to talk to Murphy; he tells her that Bobby Jack stopped in for baby supplies on the way out of town. She asks him what she should do, and he sets her straight; he is not her advisor, as there are professionals in town for that. Then he kisses her passionately, says that if she doesn't know how things are, she might not be as smart as he thought she was, puts her out the door and turns the "closed" sign up. Driving home in the truck, she thinks things over.
At home Murphy has finished his ride and stabled his horse. After he and Emma make some awkward small talk, he tells her to change her tack, but Emma admits she doesn't know what tack to take. Murphy tells her that he may be worn, but sturdy and faithful, and he is in love for the last time in his life. She replies that she is in love for the first time in her life and asks him to stay for supper, but he replies that he will only do so if he is still there for breakfast, so she says, "How do you like your eggs?"
As they go into the house together, he tells her his age. He is sixty.