• You cannot try to stealth if a creature is within 20' of you and can 'essentially'  see you (as it is observing you)
• Exception: When a creature is momentarily distracted, this requirement can be ignored at a penalty [See: Bluff]. 

• You require cover or concealment to attempt stealth.
• Exception: When you begin your turn in with cover or concealment, a successful check allows you to maintain stealth until the end of your turn (or it is otherwise broken). 

• Exception: When a creature is not affected by your source of cover or concealment (i.e. it uses Crystal Sight against stone walls, Door Sight against doors, Gaze of Flames against smoke, Darkvision or see in darkness against darkness, Goz mask against mists and fogs), that particular element will not allow you to stealth against the creature.

• You cannot stealth while running or charging. Running would be moving more then 2x your normal speed.
• When a stealthed creature makes an attack (generally described as an effect that targets a creature or the square a creature occupies) its stealth breaks once the attack has resolved.  

• Exception: "Simultaneous" attacks break stealth after all of them are made; for example, all attacks from scorching ray and Manyshot are resolved before stealth is broken.]

There is a bunch of abilities that can alter or negate the above restrictions. Common examples include:

• With Camouflage, you can attempt to Stealth without cover or concealment when you are in your favored terrain. [Note that this ability does not allow you to stealth while being observed.]
• With Hide in Plain Sight, you can attempt to stealth while being observed. [Note that this ability does not allow you to stealth without cover or concealment.]
• With Hellcat Stealth, you can treat bright and normal illumination as if it were concealment for the purposes of attempting to stealth.
• With Silent Hunter, it is possible to stealth while running.

• If a rogue can catch an opponent when he is unable to defend himself effectively from her attack, she can strike a vital spot for extra damage.

• anytime target would be denied a Dexterity bonus to AC 
• An opponent is denied their Dex when they have not acted in combat and when they are being flanked. 

• critical hit (sneak attack)  not multiplied. 
• Ranged attacks -  target is within 30'.
• must be able to see the target well enough to pick out a vital spot 
• cannot effect target with concealment

• Stealth check required, or must be in stealth
• Make one ranged attack unless feats or level allow otherwise

• Feinting is a standard action. 
• To feint, make a Bluff check. DC = 10 + your opponent's BAB + opponent's Wis mod. 
• If your opponent is trained in Sense Motive, the DC = 10 + opponent's Sense Motive bonus, if higher. 
• successful = next melee attack you make against the target does not allow him to use his Dex bonus to AC (if any). This attack must be made on or before your next turn.
• When feinting against a non-humanoid you take a –4 penalty. Against a creature of animal Intelligence (1 or 2), you take a –8 penalty. Against a creature lacking an Intelligence score, it's impossible. Feinting in combat does not provoke attacks of opportunity.