Would someone mind telling me how all these pen and paper games work?
Long post incoming, of debatable helpfulness and accuracy.
Standard pen and paper games run off of a book of rules. Each character has their own character sheet, detailing the various aspects of their character. One person - the Game Master - creates some sort of adventure or mission for the Player Characters. The GM also controls or plays as all Non-Player Characters (everyone and everything in the game that is not a player). Gameplay occurs primarily verbally, with settings and actions described by the GM; in some cases, miniatures and tabletop maps can be used to help with representation. Whenever a PC (or NPC) tries to do something that requires the use of skills, has a chance of failure, and/or would have success determined by chance, dice (of various numbers) are used; modifiers from the character's sheet and environmental/situational modifiers are added into these die rolls.
For example, here is how an instance of combat would work in many PnP RPG's: Turns in combat are decided by roll of the d20 and addition of Dexterity and additional Initiative modifiers. The PC whose turn it is decides to attack an adjacent enemy with their melee weapon. They roll the d20 to attack, and add their Strength modifier and other attack modifiers, such as weapon proficiency. This is a higher number than the target's defense (which is 10 + armor modifier + Dexterity modifier), so the attack hits. Damage is rolled - for example, 2d6 - and then their Strength modifier is added to the final damage. This number is taken off of the target's health.
Here's the Wikipedia article for
Tabletop Role-Playing Game, for further information.
Paranoia as it is run here is a bit different. The players aren't supposed to know the rules. They have a character sheet, but don't necessarily know what it means. The GM handles all rolls, dealing with modifiers. Gameplay in combat is turn-based, but (depending on the GM) not as strictly as many PnP RPG's. The GM tells everyone what everyone can see happening, but can also confer private information to only players who would know what is happening; in addition, players can tell private actions of their character to the GM, rather than performing it publicly. I'm not sure if there's a standard health system in Paranoia. Paranoia tends to be much more chaotic than many other games, often with the PC's working against each other.
Overall, in Paranoia, you say what your player does and the GM makes it so. Everything gets crazy really fast. Everyone WILL die at some point. It's really fun, and easy for anyone to get into.