Taking 10: When the character is not in a rush and is not being threatened or distracted, the character may choose to take 10. Instead of rolling 1d20 for the skill check, calculate the character's result as if the character had rolled a 10.
Taking 20: When the character has plenty of time (generally 2 minutes for a skill that can normally be checked in 1 round, one full-round action, or one standard action), and when the skill being attempted carries no penalties for failure, the character can take 20.
Instead of rolling 1d20 for the skill check, calculate the character's result as if the character had rolled a 20. Taking 20 means the character is trying until the character gets it right. Taking 20 takes about twenty times as long as making a single check would take.