Four aliens arrive on earth and assume the identities of Dick, Sally, Harry and Tommy -- the Solomon family-- for the purpose of observing life on this planet. The Solomons find an apartment in Rutherford, Ohio. Dick secures a job as physics professor at the University and finds himself strangely attracted to Dr. Mary Albright, his office-mate. Tommy is in the throes of puberty and longs to get off the planet.
When Tommy comes down with a terrible cold, the other aliens also get sick for the first time, and they're all convinced that they're dying. Dick accompanies Dr. Albright to a wedding where his eccentric behavior soon makes them the center of attention. Fearful that he may die during the night, Dick confesses that he's an alien and that he loves Dr. Albright.
When Nina inquires about Dick's birthday, he has no idea how to respond. Dick informs the other aliens that they need to know how old they are and they also need birthdays. Dick gets upset when he determines that he's past his prime, but Sally concludes that if she has to be a woman, she's at the ideal age. Nina and Dr. Albright are amused by Dicks attempts to look younger.
Dick gives Tommy an assignment to check out high school. Sally, in a quest to experience sex, goes out on a date but is be devastated when her date, doesn't call as promised. Dr. Albright and Nina take Sally out for drinks to console her about her dating problems.
Sally complains to Dick that, as second in command, she never gets to make decisions. Dick tries smoking and is instantly hooked. When Dick goes missing, Sally takes charge command and leads Harry and Tommy in a long, exhausting search for him. When they finally find him, Sally is happy to give up the role of High Commander.
Harry finds a stray puppy, and while trying to establish communication with it, falls in love. Tommy thinks he's found definitive information about male/female relationships in the comic books he's reading. When Dr. Albright responds warmly to an old friend, Dick feels jealous. Harry is devastated when Mrs. Dubcek says he has to get rid of Scruffy, the puppy.
Sally takes on the job of researching women and their beauty secrets. Tommy runs into August, a girl from school and they are mutually attracted. Harry is introduced to the finer points of skin care and opens the door to a new career. Meanwhile, when Dr. Albright leaves town for a short retreat, Dick feels devastated and abandoned.
Relations become strained between Tommy and his girlfriend August when a cheerleader, enters the picture. Dick, Sally and Harry attend a party in honor of Dr. Hanlin, an irascible faculty member. When Dr. Hanlin drops dead of a heart attack at the party, most of his colleagues are secretly relieved, but Dick is perplexed to learn that Dr. Hanlin's dying wish was for him to deliver a eulogy at the funeral.
Dick confides to Dr. Albright that he and Sally can't seem to stop fighting, and Mary tells him it's the same with her younger brother Roy. When Dick meets Roy, he immediately likes him until Roy tells a story about being abducted from a cornfield by an alien spacecraft.
Dr. Albright uses flattery to convince Dick to attend a faculty meeting in her place, but Dick alienates the group by revealing that Dr. Albright feels the faculty members are a bunch of stodgy, boring old men. Meanwhile, Harry and Sally decide that they must have drivers licenses; Tommy experiences the mall, and feels that he's found his true home at last.
Sally takes command of the bake sale at Tommy's school whips the mothers into shape and makes the sale a success. Dick and Harry attend an art class where Dr. Albright is studying painting and Harry, discovers his true talent. Dick, envious of Harry's artistic ability and declares that they won't be going back to class, but Harry stands up to the High Commander for the first time.
Harry has a new job at a video store where he takes his work very seriously. Dick convinces Dr. Albright that he should accompany her to Chicago to receive an anthropology award. They are forced to drive to Chicago in a snowstorm only to be marooned at a truck stop, missing the awards ceremony.
The Solomons decide to make contact with their neighbors the Mullers, whom they've been observing from afar. When the Solomons innocently pay a social call at 3:00 a.m. and reveal to the Mullers that they've been spying on them, Mr. Muller throws them out. Dick experiences anger for the first time. Sally and Mrs. Muller, however, continue their friendship. Dick punches Muller in the nose.
Harry joins a CD club and finds the responsibilities of membership overwhelming. Dr. Albright observes that it's virtually impossible to get a straight answer from Dick about his past. Dick chides Tommy that, as information officer, he failed to brief the crew on the sixties. Mary Albright becomes convinced that Dick is actually Manny Rosenberg, a sixties activist and who has been in hiding from the FBI for decades.
When Dick confronts Sally about her obsessive shopping habits, she decides it's time she and Harry get jobs to earn their own money. Feeling excluded when Nina and Dr. Albright do some female bonding, Dick dressed in drag, crashes a women's study group meeting in the teacher's lounge.
When Dick and Sally meet with Tommy's teacher, they learn that Tommy is having trouble fitting in. Sally wants to get to know his handsome teacher, Mr. Randell. Sally enlists Harry to teach her how to dance. Dick considers being Italian because Dr. Albright thinks Italians are sexy, and Tommy experiments with being a "bluesman".
When the aliens' car stereo is ripped off, Harry and Sally pay a visit to the police station to report it and begin discussing security measures. Dick thinks they're being paranoid, but when he gets mugged at the ATM, he demands justice. Dick insists that Tommy join the school's basketball team, but the coach thinks he's too short to play. Dick and Mary Albright have a discussion about trusting one's fellow human beings.
Harry is depressed because he feels he has no identity or purpose on the aliens' earth mission. Sally learns that Frances, Mr. Randell's extremely possessive mother, is in town for a visit. She insists on meeting her for dinner, but the meeting is disastrous and the two women wind up throwing punches in the ladies' room, with Sally coming out the loser. Harry crashes his car and ends up at the police station.
When Dick learns that Dr. Albright is getting a better office he's devastated and makes a few phone calls, as a result she loses the office. He feels vaguely guilty but assures himself that his needs come first. While teaching Sally to make guacamole, Mrs. Dubcek cuts her finger. At the hospital, the aliens begin speaking like characters from every medical drama they've ever seen. They create havoc until they're escorted out by security.
Tommy has sent a report to the Big Giant Head, informing him that Dick has been squandering time in pursuit of an earth woman. When Dick finally experiences sex for the first time he is euphoric, until he learns that the Big Giant Head is sending replacement aliens. Dick is replaced by Evil Dick, who assures Dick that nobody will notice his absence.