The plot follows high school students Alex and Ryan as they cross River City in an attempt to reach River City High and rescue Ryan's girlfriend Cyndi from the clutches of a villain called "Slick". Along the way, they battle with gangs of students (with names such as "The Generic Dudes", "The Frat Guys", "The Jocks" or "The Squids") and several gang leaders which act as bosses or sub-bosses.

River City Ransom is a beat 'em up game with action role-playing elements. The game is non-linear, allowing players to explore an open world, in a sandbox manner. The fighting style is very similar to Double Dragon, in that the player can move freely around the screen while pressing buttons to punch, kick, or jump. Objects such as brass knuckles, steel pipes, and trash cans can be used as melee weapons or thrown at enemies. However, the characters' effectiveness in battle is determined by several statistics and their knowledge of fighting techniques, such as Grand Slam, Stone Hands, and Dragon Feet, which are purchased as books in shops throughout the city using funds recovered from defeated gang members.This loot may also be spent on various food items and spa treatments which serve to not only revitalize the player's stats, but may also permanently increase attributes like "Punch" and "Kick" (Foods and items offer varying levels of improvement).

The player can input passwords that keep track of their character's stats, skills, possessions, money, and defeated bosses. There are a total of nine gangs in the original NES version (which are distinguished by the color of their t-shirts) whom the player will encounter during the course of the game, each with their own characteristics and attacking patterns.