The whole story starts here as Gordon Shumway, a Melmacian who escaped his planet before it was destroyed, crash lands into the garage of the Tanner family. The Tanners call him “ALF” because he is an Alien Life Form and they decide to keep his presence a secret so that the U.S. Government will not take away the space being and subject him to experiments. From the beginning, there is no sanity for the Tanner family.
Everybody but Brian and ALF are leaving the house for the evening and Kate doesn't want ALF to babysit Brian, so Willie calls their ever-snooping Mrs. Ochmonek from the neighbor. ALF is told to stay in the bedroom, but when Mrs. Ochmonek starts to watch Psycho, which ALF wants to see, he can't resist sneaking out of the bedroom. Mrs. Ochmonek is in for some unusual experiences.
Lucky is missing and the evidence suggests that ALF ate Lucky, although he claims to be innocent.
Gordon (A.L.F.), having lost his planet in an explosion, becomes very concerned about earth's nuclear proliferation. He uses Willie's short wave radio to contact the President of the United States aboard Airforce One - to the great displeasure of the FBI.
Gordon (A.L.F.) is insulted when the Tanners consider him a parasite, free-loader, sponger. He tries to make money to be less of a burden on the family, but puts Willie's VISA card over the limit purchasing “Terry Faith Cosmetics” to sell at a house party.
Alf becomes the friend of a lonely blind woman.
Brian's 7th birthday is approaching and it gets ALF depressed, because he realizes he's never going to see his friends on Melmac again - he was finally going to get together with his true love Rhonda and then the planet exploded. In sleep, ALF dreams about his 228th birthday on Melmac, just before the explosion. In order to cheer ALF up, Brian and Willie start broadcasting into space, in hopes of finding another survivor from Melmac.
Lynn is excited because “Scott” wants to keep all his band equipment in the Tanner's garage. Willie is not so excited. Lynn is interested in Scott and begs for Willie to allow Scott to keep the equipment in their garage for just two days. Willie gives her his permission. ALF is not happy - he was supposed to be re-decorating his room with Lynn. And he also has a crush on Lynn, so he proceeds to sabotage Scott's time with Lynn while trying to come up with something to impress her.
It's Willie's birthday. ALF gives him a box he found in the basement. It's full of photos from high school and college. There's also a menu, on the back of which Kate and Willie both made lists of things they wanted to achieve in life. Kate actually did the things on her list, but Willie did not. This starts to haunt him so badly that he decides to do the list.
Lynn is going to a concert with her friend and is waiting to get the car for the evening… but Willie and Kate are late and the girls are in danger of being late for the concert. Then Willie and Kate arrive… with the help a tow truck. The tow truck man estimates that the repairs will cost way over 3,000 dollars - not good. Lynn is upset and wishes for another car. ALF asks why Willie doesn't buy Lynn a car and Willie has to explain that they can't afford it - especially since a lot of money went into repairing the garage roof because ALF crash-landed on it. Lynn …
Willie suggests that they go to San Diego on holiday. Kate is all for it, but there's a slight problem: what to do with ALF? Since leaving ALF alone is a recipe for disaster, the family takes him along for the road trip. However, the weather turns stormy, ALF gets bored of sitting in the RV and starts complaining. Willie goes mental and shows ALF the door. Defiantly, ALF wanders off.
It's Christmastime. Unfortunately ALF chops the Christmas tree into firewood before anyone notices. The Tanners then have two tasks: to teach ALF all about Christmas and find a new Christmas tree.
Kate's mother, who is not on warm terms with Willie, arrives for a surprise visit that forces the Tanners to lock ALF in the garage for “a few days”. The problem is that ALF just can't stand being not allowed to roam around in the house, with all the luxuries found there. So he just has to do something.
ALF and Kate's mom are arguing about TV. Kate's mom thinks ALF's favorite soap opera, Midwest General, is sleaze, and shows him her favorite, One World to Hope For, which ALF thinks is boring. Angered, ALF argues that he could write a better script for the series than the writers are coming up with. So ALF actually writes a script and sends it in. The production company actually films ALF's script that bears not-so-subtle similarities to the situation at the Tanners' house…
Willie catches ALF from eating a box of chocolate that was to be a Valentine's Day present for Kate. This incites Willie to give ALF a lecture on how ALF does not respect private property and needs to adopt a new attitude. Also, Kate's mom is moving out of the Tanners' house. The problem is that her new neighbor, Whizzer, wants to come help Dorothy move her stuff. Which means ALF has to hide from him. Kate likes Whizzer and suggests that they invite him over for a dinner. Dorothy doesn't want that. ALF interjects by claiming to have spoken to Dorothy's dead husband …
ALF bumps his head and loses his memory. All he knows is that his name is Wayne Schlagel and that he's an insurance agent. The Tanners try to make ALF remember who he really is - cue clips from earlier episodes.
ALF is now into gardening, which means he's turned over the entire Tanner's backyard. Willie has a problem at work: a lost Mexican boy is at his office and Willie is trying to track down his father. When that fails, and Willie's boss couldn't care less about helping the boy, Willie has no option but to bring the boy home.
ALF starts to go through a phase where his erratic behavior and hunger for cats will, in his own words, make him “ALF to the tenth power”. He wants Willie to build a cage where he can be locked in until the phase is over. Will the cage be strong enough? Can they keep him locked in when he tries to plot himself out?
Brian has to lie to his friend who wants to come for a sleepover that the Tanner's basement is flooded, because ALF must be kept secret. Willie then tries to explain to Brian that lying is always wrong even though Brian has to keep lying because of ALF. Lying to the Ochmonecks is also tiring Willie, not to mention having to put up with ALF's antics. Kate suggests Willie talk to Larry, a therapist they know. Of course, Willie has to prove that ALF exists and is not his hallucination, which means that Larry and ALF meet.
There's a power blackout, so ALF is passing the time by watching the Tanners' neighbors, the Ochmoneks, who are fighting. By dinner time, the power has come back so the Tanners can have dinner. Then comes another, short blackout. Trevor Ochmonek appears at the Tanners' door, seeking peace and quiet from the angry Raquel. Soon after, Raquel comes to demand that Trevor return home. The Tanners persuade him to do so. Night falls and ALF hears the Ochmoneks continue fighting. Suddenly it becomes silent. Too silent for ALF, who's convinced that something foul has happened …
Lynn has introduced ALF to rap music, much to Willie's dislike. Willie himself is making the final changes to Brian's song in the school pageant where the kids dress as vegetables. Unfortunately, Brian is suffering from stage fright, which causes him to forget the lyrics. ALF offers to help…
The Tanners are preparing for a garage sale to get some money for house payments. ALF discovers the alluring world of horse racing thanks to Kate's mom who bets on them. When the concept of a bookie is explained to ALF, he gets the bright idea of getting the Tanners some money through betting. When his initial bets yield only profit, the plan seems good… at the time.
When the living room TV breaks down, Willie declares that he won't have it fixed, despite ALF's complaints that he has nothing to do but watch TV. ALF keeps pressuring Willie, who discovers that the TV is still under warranty and he can have it sent to the factory for repairs. Except that the factory is in Libya and Willie would have to pay for shipping… ALF thinks Willie has been conned, so he calls Consumer Ed, the guy who fights for consumers' rights on TV… Brian announces that he needs to come up with a project for the Science Carnival. On his own, Brian …
An insect from Melmac has an unexpected reaction when exposed to earthly chemicals.
ALF thinks he's won in a publisher's sweepstakes, but the actual truth is that he subscribed to “hundreds of magazines” (Willie probably exaggerates here)… The next leaflet ALF gets his hands on *does* promise free gifts, but only if the family comes to listen a sales pitch for vacation homes. The Ochmoneks are going there, so Trevor invites the Tanners to come along. Turns out he is a pilot who flew in the Korean war, so they are able to fly instead of a seven-hour drive. The reluctant Willie eventually warms to the idea, but ALF has to stay home. Or is it that he …