Rolling a natural 1 on a skill check is considered an automatic failure. It is up to GM's discretion whether the failed check has other implications.
Rolling a natural 20 on a skill check is not usually considered an automatic success. If it is a success, it is up to the GM's discretion whether to consider it a particularly special success.
NOTE: If rolling a natural 20 and adding the skill check modifier would still be a failure, there's no reason to roll the skill check in the first place.
In certain circumstances, rather than the PC rolling a skill check against a fixed environmental DC, he make an opposed skill check in which both you and the PC roll against each other to see who wins. An opposed check is usually used in cases where there is an active entity going against the players and that entity is potentially unpredictable, such as an NPC.
In these cases, both parties roll the appropriate skill check. Whoever gets the higher result succeeds.
Under certain conditions, a player may choose to perform a special kind of skill check where the skill being used can be based on a different ability check. For example, a player might want to use their imposing physical presence to intimidate an adversary, so although intimidation is generally a Personality (Speechcraft) skill check they might want to use Strength as the base attribute for it.
In these cases, when determining the skill check modifier you use the base ability and add any proficiency the player has in the specific skill.
This skill check is usually designated in the same manner as a normal skill check, which shows the ability followed by the skill. For example, in the above case it would be a Strength (Speechcraft) skill check.
Athletics: Climbing, escaping from a grab, jumping high or long distances, swimming or treading water
Acrobatics: Perform an acrobatic stunt (swinging from a chandelier, somersault, etc.), escaping from a grab, maintaining your balance, reducing damage from a fall
Driving: Steering a car, performing advanced driving maneuvers
Piloting: Piloting an aircraft, performing advanced aerial maneuvers
Stealth: Hiding from enemies, remaining undetected, moving silently
Thievery: Pickpocketing, palming an item, picking a lock, escaping restraints,sleight of hand
Endurance: Resisting harsh weather and temperatures, holding your breath, ignoring thirst or hunger, resisting poisons and toxins, tolerance to radiation exposure
Investigation: Interpreting clues, analyzing objects
Lore: Recollecting information from the past. Knowledge of history, culture, religion, etc.
Mechanics: Interacting with machinery that has moving parts, repairing a vehicle
Medical: Providing first aid, stabilizing a dying creature, identifying wounds and other symptoms
Technology: Interacting with computers, understandint and using advanced technology
Animal Empathy: Pacifying wild animals, controlling a mount under adverse circumstances
Insight: Interpreting body language during social interactions, discerning intent, detecting lies, getting a sense of mood or demeanor
Perception: Noticing visual clues and things that are out of place, detecting hidden objects, detecting hazards and finding traps, listening for sounds
Survival: Foraging for food and drink, surviving a hostile environment, searching for and following tracks
Charm: General demeanor in social situations, social graces, perform for a crowd
Speechcraft: Haggle for pricing with vendors or customers, negotiate a deal, intimidate an adversary, convince others in a social situation
