So how do you play this thing?
MM: AOH works off of a d20 system. This means that the actions in the game are executed by rolling 1 20 sided dice to beat checks against a predetermined number as defined by the DM or Dungeon Master.
A practical example:
Ash wants to grab the boom stick from the floor before the dead-ite can get to it. They both roll an ATHLETICS CHECK to see who grabs for the thing faster. They both roll a 10, however, Ash has a +0 to athletics in his stats, while the deadite has a +2. Therefore the deadite has actually rolled a 12, and beats Ash’s 10.