Basically a 20-sided die is rolled to see if there is a chance for a wild pitch, balk, or passed ball. If the right number is rolled, then the 20-sided die is rolled again to see if one has occurred. There is a little bit more to it than that; here are the exact rules concerning wild pitches and balks (and passed balls):
Individual Wild Pitches and Passed Balls
Whenever there is at least one runner on base you should use the following rule: When rolling the three dice to read the results off of the players cards (or when using the hit and run chart) you should roll a 20-sided die along with the three dice. If a 3 to 20 is rolled , continue on with the normal reading of the three dice (if a split reading occurs you MUST re-roll the 20-sided die) If a 1 or 2 is rolled then the normal reading of the other dice is canceled and a wild pitch, balk or passed ball may occur.
A roll of 1 on the 20-sided die indicates that a wild pitch may occur. Roll the 20-sided die again and refer to the pitcher's wild pitch rating. If the number rolled is less than or equal to the pitcher's wild pitch rating then a wild pitch occurs and all base runners advance 1 base.
A roll of 2 on the 20-sided die indicates that either a balk or a passed ball may occur, Refer to the single white die and if it reads 1 to 3 a balk may occur, If it reads a 4 to 6 a passed ball may occur. In either case roll the 20-sided die again and refer to the appropriate rating (the pitcher's balk rating or the catcher's passed ball rating). If the number rolled is less than or equal to the appropriate rating then a balk or passed ball has occurred and all base runners advance 1 base.