For the first two seasons it seems that there was someone inside an ALF suit.
An actor called Michu (Mihaly “Michu”) Meszaros (Wikipedia link) who was on 2ft 8in tall
For the first season of the ALF television series, Meszaros donned a costume whenever a full-body shot was needed for scenes of the alien walking, running, or standing. For the most part, however, upper-body shots of a mechanical puppet were used instead, since the full-body costume was extremely hot and uncomfortable for the actor to wear for long periods of time under bright studio lights. The ALF puppet and costume can be distinguished on first view because the head proportions are slightly different.
From an interview:
Q: What was it like working on “ALF,” and was that costume uncomfortable?
A: It was hot. They were trying to keep it a secret that I was inside the costume. My manager took this picture of me in the costume holding the head. He knew that the show would be very famous and wanted proof that I was inside of ALF.
Q: How many seasons of the show did you do?
A: I left after two years. They fired me. I never found out why. Overnight it went from me being in the ALF suit to no more!
They were trying to get me out after the first year. They wanted to use puppets and robotics. The producer didn’t like me for some reason.
For the first two seasons of the show, there was a little person inside of an ALF costume for any full-body scenes. At one point, 33-inch-tall Mihaly “Michu” Meszaros was listed in the Guinness Book of Records as the world’s shortest person. And while life in his native Hungary as a youth was brutal (thanks to unscrupulous circus owners), a day in a furry costume under hot studio lights may often have been worse.
Any close-ups or talking shots of ALF were a puppet operated by the alien’s creator, Paul Fusco. The entire soundstage was built on a four-foot-high platform so that Fusco could sit underneath it and make ALF move and talk through one of the dozens of trap doors that were cut through the floor.
After that it seems the show creators went to puppets and robotics.