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.
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.
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.