Skills
A character's skills represent a variety of abilities. As a character advances in level, s/he gets better at using some or all of the chosen skills.
To accomplish something using a skill, there is a Difficulty Class (DC) that must be met or exceeded in order to successfully use the skill. A skill use requires a 1d20 roll, then add the rank the character has in that skill, the ability modifier for that skill, and any miscellaneous modifiers for that skill. If the roll + rank + ability mod + misc mod matches or exceeds the difficulty for the task, you succeed.
Ranks
There are a maximum number of ranks that a character can have in any given skill, which is equal to 3 + the character's level. For example, a lvl1 character can have a maximum of 4 ranks in any given class skill and a maximum of 2 ranks in any given cross-class skill.
There are two types of skills: class and cross-class. Each character class has a set of skills that are natural abilities for that class; all other skills are not natural for the class. A rank in a class skill costs one skill point. A rank in a cross-class skill costs two skill points.
Use of Skills
Some skills can be used untrained, so you don't have to buy ranks in them to have a modifier to use on your skill checks.
Two skills can work in opposition. For example, a character using a Move Silently skill to sneak past a guard has to beat the guard's Listen check in order to successfully sneak by.
Most skills can be attempted multiple times, which requires multiple skill checks. However, if the character is not being influenced by some sort of distraction, s/he can choose to "take 10"; if there's no distraction, no penalty for failing a skill check, and plenty of time, the character can choose to "take 20" instead of rolling repeatedly; this choice assumes that the character tries to accomplish the task repeatedly and fails at least a few times before completing the task successfully.
Favorable and unfavorable conditions can affect the dice rolls, as well. For example, a thief with a Thief's Tool kit gets a +2 circumstance bonus on any thieving activities because of having the perfect tool for the job (having to improvise a tool to do a job results in a -2 circumstance penalty instead). Favorable conditions, such as a friendly audience for a performance, reduce the DC for a performance check; a hostile audience increases the DC.
Most of the time, skill checks apply to only to the character making the check. However, characters can get assistance for some tasks, such as healing; this only applies if the assisting character could make the skill check on his/her own.
Some skills are synergistic, such as Bluff and Diplomacy. Once a character has 5 or more ranks in a synergistic skill, it provides a +2 bonus to another skill.