The core mechanic utilizes a simple lookup table. It tells you what you need to roll on a d20 in order to succeed on any given task.
The table features a built in “bell curve” that gives equal odds to evenly matched opponents but makes hard stuff easier and easy stuff harder so that nothing is impossible and nothing is too easy. There is always a chance of failing the simplest of tasks, and there is always the chance of beating even the toughest foe.
The table works for combat, spell casting, attribute checks, skill checks, and everything.
Here's a PDF download for you: Letter Size Success Table PDF
It's very easy to use. Whatever task you are attempting will have an associated skill number or attack number. Find that number on the left orange Attack axis. Place your left finger on that number.
The task you are attempting will have a Difficulty or Defense number. Find that number in the top blue Defense axis. Place your right finger on that number.
Move your fingers across from the left to the right and down from the top, until your fingers meet. The number in the square where they meet is your success role target number. This is the number you need to beat (or match) on a d20 roll. If you roll higher or equal to this number, you succeed. If you roll lower, you fail, try again on your next turn.
It's probably easier to just see some examples of the chart in action: