The basic gist, without rewriting the whole (one page) rulebook:
STEP 1: You come up with a character concept. The GM gives you points.
EX: You are Mario, the GM gives you 100 JUMPING and 50 FIRE FLOWER.
STEP 2: You play. Whenever you do something that requires a roll, the GM decides which points you would have to spend and the difficulty of the roll in number of dice. i.e. 1d2 (coin flip) is an extremely easy action, whereas 5d20 is something rather difficult. The player then spends whatever amount of points he chooses, and if the roll is less than the amount the player spent, the action is successful.
EX: You try to jump over Bowser. The GM considers this a 6d20 roll for JUMPING (I guess he's Sunshine scale Bowser, whatever). You spend 60 points. The roll is 52, so you succeed, and now have 40 JUMPING.
STEP 3: The GM arbitrarily rewards extra points whenever he pleases. The GM can never take points away.
EX: The GM is impressed by your jumping, and rewards you 80 JUMPING and 10 DOING THE PRINCESS points, so you now have 120 JUMPING, 50 FIRE FLOWER and 10 DOING THE PRINCESS.
STEP 4: Repeat.
The actual flow of the game is radically different from GM to GM, as each one will invariably come up with his own subtle rules for gameplay. I, for example, tended to break the quest up into "chapters" and refresh everybody's points after each one. I also allowed a lot of auto-success roles (i.e. spending 20 points on a 1d20 roll) and let players do whatever they liked as long as they could justify it (my favorite: Napolean using his powers of dictation to declare a state of Deus Ex Machina, which in effect summoned a bear). Kazz did... something else.
And that's how you play FFAGS.