Skills represent some of the most basic and yet most fundamental abilities the character possesses. As a character advances in level, they can gain new skills and improve their existing skills.
Each level, a character gains a number of skill ranks dependent upon their class plus their Intelligence modifier. Investing a rank in a skill represents a measure of training in that skill. Character's can never have more ranks in a skill than their total number of Hit Dice. In addition, each class has a number of favored skills, called class skills. It is easier for a character to become more proficient in these skills, as they represent part of his professional training and constant practice. Characters gain a +3 bonus on all class skills that they have ranks allocated to. If a character has more than one class and both grant a class skill bonus, these bonuses do not stack.
The number of skill ranks a character gains when taking a level in one of the base classes is shown on Table: Skill Ranks. Humans gain 1 additional skill rank per class level. Characters who take a level in a favored class have the option of gaining 1 additional skill rank or an additional hit point. If they select a level in a new class, all of its class skills are automatically added to their list of class skills, and a character gains a +3 bonus on these skills if they have ranks in that skill.
When character uses a skill, they aren't guaranteed success. In order to determine success, whenever they attempt to use a skill, they must make a skill check.
Each skill rank grants a +1 bonus on checks made using that skill. When a character makes a skill check, they roll 1d20 and then add their ranks and the appropriate ability score modifier to the result of this check. If the skill they are using is a class skill (and the character has invested ranks into that skill), the character gains a +3 bonus on the check. If they are not trained in the skill (and if the skill may be used untrained), they may still attempt the skill, but they use only the bonus (or penalty) provided by the associated ability score modifier to modify the check. Skills can be further modified by a wide variety of sources - by their race, by a class ability, by equipment, by spell effects or magic items, and so on.
Taking a 10 and Taking a 20
A skill check represents an attempt to accomplish some goal, usually while under some sort of time pressure or distraction. Sometimes, though, a character can use a skill under more favorable conditions, increasing the odds of success.
Taking 10: When a character is not in immediate danger or distracted, they may choose to take 10. Instead of rolling 1d20 for the skill check, calculate the result as if the character had rolled a 10. For many routine tasks, taking 10 makes them automatically successful. Distractions or threats (such as combat) make it impossible for a character to take 10. In most cases, taking 10 is purely a safety measure - the character knows (or expects) that an average roll will succeed but fear that a poor roll might fail, so the character elects to settle for the average roll (a 10). Taking 10 is especially useful in situations where a particularly high roll wouldn't help.
Taking 20: When a character has plenty of time, the character is faced with no threats or distractions, and the skill being attempted carries no penalties for failure, they can take 20. In other words, if a player rolls a d20 enough times, eventually they will get a 20. Instead of rolling 1d20 for the skill check, just calculate result as if you had rolled a 20.
Taking 20 means the character is trying until they get it right, and it assumes that you fail many times before succeeding. Taking 20 takes 20 times as long as making a single check would take (usually 2 minutes for a skill that takes 1 round or less to perform).
Since taking 20 assumes that the character will fail many times before succeeding, the character would automatically incur any penalties for failure before they could complete the task (hence why it is generally not allowed with skills that carry such penalties). Common take 20 skills include Disable Device (when used to open locks), Escape Artist, and Perception (when attempting to find traps).
Ability Checks and Caster Level Checks: The normal take 10 and take 20 rules apply for ability checks. Neither rule applies to concentration checks or caster level checks.