Alien life form Gordon Shumway crash lands into the garage of the Tanner family. The Tanners call him "ALF" 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.
When everyone is leaving the house for the night except Brian and ALF, Kate doesn't want ALF to babysit him, so they ask Mrs. Ochmonek to babysit. When Mrs. Ochmonek starts to watch Psycho (1960), ALF tries to sneak out of the bedroom.
ALF, 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 aboard Air Force One - to the great displeasure of the FBI.
ALF is insulted that the Tanners consider him a parasite. He tries to make money to be less of a burden on the family, but puts Willie's credit card over the limit purchasing "Terry Faith Cosmetics" to sell at a house party.
To cheer up the sad ALF, Brian and Willie start broadcasting a message into space - and are very surprised when old friends of ALF answer them and offer to pick up ALF.
When ALF finds an old bucket list of Kate and Willie, Willie starts to have second thoughts about the things he did not do in life - he decides to do a parachute jump he always wanted to dare.
Leaving ALF alone is a recipe for disaster so the family takes him along in the RV. The weather turns stormy and ALF gets bored sitting in the RV and starts complaining. Willie goes mental and kicks out ALF. In defiance, ALF wanders off.
It's Christmas time. 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 as well.
Kate's mother arrives for a surprise visit that forces the Tanners to lock ALF in the garage. The problem is that ALF just can't stand being not allowed to roam around in the house, so he just has to do something.
Dorothy thinks ALF's favorite TV soap opera is sleaze, and shows him her favorite which ALF thinks is boring. Angered, ALF argues that he could write a better script than the writers. So ALF actually writes a script and sends it in.
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.
ALF still believes that his name is insurance agent Wayne Schlagel and has also called the police to the Tanners. The Tanners have only a short while, so they try to make ALF remember who he really is by telling more stories from the past.
While ALF now is into gardening, 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, Willie has no option but to bring the boy home.
ALF enters a phase where his erratic behavior and hunger for cats will, as he says, make him into a lunatic. He wants Willie to build a cage where he can be locked in until the phase is over. But ALF has the great ability to deceive.
Willie is making the final changes to Brian's song in the school pageant where the kids dress as vegetables. Unfortunately, Brian forgets the lyrics. ALF, who has been introduced to rap music by Lynn, offers to help.
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.
Brian 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.
When ALF wins a free weekend at a vacation home, Trevor offers to fly everyone there with his plane. ALF, who doesn't want to pass on the free holiday, smuggles himself aboard as cargo.
