Typically the metal screws in the face plate/trim of a home electrical device (outlet, light switch, etc.) attach to the electrical device itself. This, in turn, should be grounded.
To address your question in general (the spirit of what you're after):
If it only shocks you one time, which is to say if you touch it and it shocks you, but subsequent touches without moving don't continue to shock you, then I would say that you are getting a static electricity shock because the screws in the trim plate are grounded and you are not. This would be more likely if you have carpet, the air is dry, and/or you are wearing clothes that are wooly and/or you don't use dryer sheets.
If you get shocked (badly - shocks from 110 HURT!), and every time you touch the screw you get shocked (badly!), then you have a serious problem and should contact an electrician.
Most likely, though, you're just experiencing drier air because Winter's coming and the dew point is dropping while your interior temperatures are staying relatively constant. Every winter every outlet in my house shocks the **** out of me. But only the first touch. Subsequent touches don't do anything because I discharged my static buildup.
To answer your numbered questions:
Turn off the breaker to the offending outlet, remove the trim screw, remove the retaining screws that hold the device into the wall box, then pull the device out. Check for problems with the insulation - you may find these where the cable enters the junction box - and for bare wire ends touching the junction box. If you have a multimeter (not sure if most people would consider this a common household tool, though it should be!), then you can try turning the breaker on and measuring voltage between the ground wire in that device to ground in another outlet.
If there is a real problem, contact a licensed, bonded electrician. You may need new wiring pulled to the offending device if the insulation is frayed/nicked where it enters the wall box.
Yes, other things can cause you getting shocked - primarily the fact that the outlet is grounded correctly. Though I suppose maybe if your building has a ground wire that isn't grounded, and the thing that's shocking you is a doorbell or something else outside, and you're standing in a puddle, and that is when you get shocked, that maybe you're getting shocked by some piece of deranged (damaged and/or improperly grounded) piece of equipment somewhere else in your building that is powering the ground wire. But, in this case, the ground wire would have to go nowhere, else the deranged equipment would be safely handled, which is the point of the ground wire.
Anyways, like I said, ultimately the shocks are (annoying but) one-time events that don't hurt that bad and are nothing to worry about, or they happen repeatedly and hurt very bad and you should contact an electrician.