For a simpler resolution mechanic, the following can be used with minimal fuss:
The DM sets a base chance, based on his best judgement. For simplicity give the odds as intervals of 10. A tough action might be 30 percent while a specialty of a character might be 60.
To this the player adds the relevant ability score. For example a cleric deciphering an ancient religious text might get a base 20 chance but add his Intelligence. If he has a 13 INT, he'd have a 33 percent chance of success.