Beaver has lost his lunch money three times recently and gets "yelled at" by his dad, Ward, although Ward would deny that. Then Beaver is trusted with a dollar seventy-five with which to get a haircut. But, fidgeting in his seat at the barber shop, he manages to lose that money too. He tries bartering with the barber - asking if perhaps he'll take a nifty doorknob in exchange for a haircut, but the boss is away and the barber can't do that.
Beaver comes home, pilfers June's scissors, and tries to cut his own hair. Initially it's not so bad, but he is discovered by Wally who attempts to fix matters with disastrous results. Wally and Beaver - now in this mess together - decide to both wear caps for a week and tell their parents it is part of the initiation into a secret club.
The real problem here is that there is a school holiday festival and presentation coming up very shortly, Beaver is slated to be an angel, and looking like he was attacked by a lawn mower is likely to distract the audience. This episode was first broadcast in October, which was an odd time to have a (somewhat) Christmas themed show.
I like how Beaver and Wally stuck together and did not blame each other for their joint predicament, always role models for siblings working together, even if not for the best or smartest purpose.