The Core Mechanic of Dead Simple is add the Aptitude in a skill (derived from the core attributes) and the Training level in that skill, then try to roll less than that on 1D20. Other modifiers may apply such as initial bonuses from race and profession.
This is a limited system in that eventually, as your character progresses, you are going to get an Aptitude + Training + others of 21. Then what?
In SOE21 I have proposed using a more open system. In this you roll 1D20 and add both Aptitude and Training level to the score. The objective is to score 15 or more.
With a system like this it is easier to apply negative situational modifiers such as an opponent's DEX in combat.
In our current system Fighter with STR 3, INT 1 who is trained in Fighting gets 2+3+1+1 = 8. There is a 35% chance the player can roll less than this. If the Opponent's DEX is +2 this reduces to 25%.
In the alternative system the same Fighter would roll 1D20 and add +8 to his roll meaning he has to roll 7 or better to get a score of 15 and succeed. Which means he has a 65% chance, which goes down to 55% if the opponent's DEX is +2.
Some common modifiers I use when playing
Point Blank range: +1
Beyond Effective Range: -1
Poor Visibility: -2
Target in soft cover: -1
Target in hard cover: -2
Zero-g (most weapons): -4
Zero-g (laser weapons): -2
Outnumber opponent: +2
Unstable footing: -1