The plots of most episodes revolve around two central ideas: helping keep ALF hidden from the outside world and ALF helping out the Tanners through difficult and strange situations. Most episodes also involved keeping ALF away from the Tanner's pet cat. According to ALF, cats are to Melmacians; what cows are to humans. A popular food item that can be served in a variety of ways. The comedy of the series came from many varied sources, like ALF trying to fit in or Willie (Max Wright) trying to fix some problem ALF has created.
The first season consists of 25 half hour episodes. For all the troubles that supposedly plagued the production (you can read about those at other places) of the show, the episodes are well put together. Many stories were adapted from the popular culture of the time or from other notable science fiction stories. Lots of parody and introspective looks at American behavior. Episodes that featured conflicts revolving around the Tanner family usually involved ALF finding a solution to their problem, about the only real antagonisms that exist in the first season are between Kate (Anne Schedeen) and ALF, but that friction mellows out along the way. The Tanner's are probably painted a little bit too ideal than your typical suburban household. The conflict ALF causes to break up the family unit doesn't ever really last. I suppose that is why the stories are not all that deep.
Aside from lack of serious family conflict or problems, ALF provides enough excitement to the otherwise dull suburban family life. Another thing to note is that Willie Tanner is a social worker. For the life of me, I can't really think of any other show from the same time period that featured one of the main characters as a social worker. As far as government workers go, it is not really a profession portrayed much on television. Right now, the only show I can think of is perhaps the Comedy Central show Ugly Americans.
If you watched ALF growing up, remember that the plots and conflicts are not all that sophisticated. This by no means makes it a bad show per say, but if you are more of a sophisticated plot story driven viewer you might get tired with the show after a few episodes. My best advice to someone that has never seen ALF is to watch the first three episodes. If you find yourself laughing stick with it for another three. There are some nuggets of parody and satire laid underneath all the cat eating jokes. So do not fret you comedy snobs, even you will find something worth laughing at in ALF.
Also be sure to check out the Tanner's neighbor. She will later play another great supporting character on NBC's Seinfeld.