Gordon Shumway, a Melmacian who escaped his planet Melmac 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.
Everybody but Brian and ALF are leaving the house for the evening. Kate does not want ALF to babysit Brian, so Willie asks their ever-snooping neighbor, Mrs. Ochmonek. ALF is told to stay in the bedroom, but when Mrs. Ochmonek starts to watch Psycho he cannot resist sneaking out of the bedroom to watch.
Brian's 7th birthday is approaching and it gets ALF depressed because he realizes he is 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. When he falls asleep, 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 her boyfriend Scott wants to keep all his band equipment in the Tanners' garage although 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 and Willie gives her his permission. ALF is not happy because he was supposed to be redecorating 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. He also films a music video for her ("You're the One Who's Out of This World") to prove it.
For Willie's birthday, ALF gives him a box he found in the basement full of photos from high school and college. There is 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.
Willie suggests that they go to San Diego on vacation. Kate is all for it, but the family is unsure what to do with ALF. ALF starts a kitchen fire, and the Tanners realize leaving ALF alone is a recipe for disaster. Brian suggests going deep into the woods where the Melmacian alien won't be seen, and the family decides to go camping, and takes ALF along for the road trip. However, ALF drives the RV into the forest and the weather turns stormy. In the RV, ALF causes chaos as Willie is trying to be positive. This leads to Willie getting upset and telling ALF to leave and ALF wanders into a cabin nearby. Two guys who live in the cabin discover the alien and believe he is an anteater and attempt to butcher him. One of the guys discovers that ALF can talk and then Willie comes by to rescue the alien. The episode ends in the living room where ALF is showing pictures of the family vacation to Lucky.
ALF spends his first Christmas on Earth. ALF cuts the Tanners Christmas tree into firewood and Willie tries to find another tree. However, the only tree he can find is a lifelike simulated tree, but proves to be underwhelming to the family and ALF. ALF and Willie decide to go to a real tree forest to cut down a Christmas tree. However, the car breaks down in the forest and they get stuck. Willie has a dream where ALF comes in and tells Kate that the tree is a fake. Willie wakes up and realizes ALF cut a tree and put it in the car.
The episode title is based on the German Christmas song "O Tannenbaum".
Kate's mother Dorothy (Anne Meara), who is not on warm terms with Kate, arrives for a surprise visit that forces the Tanners to lock ALF in the garage for several days. The problem is that ALF cannot stand being not allowed to roam around in the house, with all the luxuries found there. So, Kate and Willie decide to introduce Dorothy and ALF.
Dorothy thinks ALF's favorite TV 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.
ALF loses his memory and thinks he is insurance agent Wayne Schlegel after accidentally electrocuting himself in the bathtub. The Tanners then use flashbacks to restore his memory.
Note: This is a one-hour clip show; later edits changed the cause of ALF's memory loss from electric shock to a head injury after NBC received complaints from viewers.
ALF, beginning to go through a Melmacian psychological and physiological transformation which happens every 75 years for Melmacians on March 2nd, warns the Tanner family that he must be locked up for 24 hours during this period in which he will experience wild, erratic behavior — but he escapes before the day is over.
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.
When the living room television breaks down, Willie declares that he will not have it fixed, despite ALF's complaints that he has nothing to do but watch television. In the meantime, Brian announces that he needs to come up with a project for the Science Carnival. On his own, Brian creates a model of the Solar System. ALF points out that there are inaccuracies and offers to help. He tells Brian that there are two more planets named Dave and Alvin.
The episode title is based on the Oingo Boingo song popularized by the movie of the same name.
ALF gives The Tanners a real estate promotion for a sales pitch and Willie opposes the idea of going on vacation and leaving ALF at home when Trevor Ochmonek offers to take them on his plane. Eventually, he decides to go on vacation with the Ochmoneks and leaves ALF at home, but ALF sneaks into the luggage and shocks Willie when the alien surprises the Tanners at the hotel. ALF accidentally burns the hotel room trying to cook catfish in the talking toaster he obtained causing the Tanners and the Ochmoneks to be thrown out of the hotel. Trevor gets an allergic reaction while flying the plane from eating shellfish that Raquel warned him about and passes out where he starts acting loopy. Now the Tanners are in danger and ALF decides to fly the plane and saves the Tanners from danger.
