The movie "Buck Privates" from 1941 is about Abbott and Costello being in the Army. They play Slicker Smith and Herbie Brown, two guys who get in trouble with a cop and try to get away by joining the Army and then end up having the same cop as their drill instructor. They would later make other military comedy films with "Keep 'em Flying" and "In The Navy" which had Air Force and Navy themes instead of the Army.
Abbott and Costello start out as salesmen who don't have a licence and that is how they get into trouble. They are more like likeable con men. They also try to con their way out of the Army but that doesn't work. They are in for the duration and go through boot camp and a training exercise that is my favorite part of the movie.
Outside of the many different Abbott and Costello routines that they do mixed into the movie, there is also singing from the Andrews Sisters and a three way love triangle story with other characters in the movie. Mostly it is great for seeing Abbott and Costello at their best because classic comedy routines are much funnier seen in the context of a good film than just watching on a stage without any support or background story.
This was happening during the draft for World War II so Abbott and Costello joining the Army to get out of trouble with the law isn't as strange as it would be today. It is what follows with a classic comedy team in basic training, even if unrealistic, is the makings of great comedy moments and a film to be enjoyed no matter what your age.