Ok, so we've talked about what GMs do and what triggered players do, but what about the other players? Being around someone who has been triggered can be very upsetting, particularly if you're the one who unintentionally triggered them. (If you intentionally triggered them without their explicit permission, go fuck yourself, you are bad and should feel bad.)
However, for the rest of us in the decent part of the human race, what do you do?
Don't freak out.
Yes, it is upsetting. It can even be scary depending on how well you know them and how they react to the trigger. Like I said in the first post, not everyone cries when triggered. Some people get violent, rarely, but it does happen.
First, once they've tapped out and are able to listen (have come back from the break, gone to the bathroom and cried, come back wrapped up in a someone else's hoodie), apologize.
No, you did not mean to trigger them, fellow decent human being, but you did. As the saying goes, "You may not have stepped on my foot on purpose, but you still broke my toe." Apologize sincerely, and once.
I have trouble with that once part. But try to rein it in and hold it to one.
Something along the lines of, "I am sorry I triggered you with the actions/situation I described. I'll do my best to remember that this is a trigger for you and not do it again."
No need to fall on your sword, or pledge undying fealty, just, "I'm sorry. I'll try not to do it again."
The next thing is: Respect their boundaries.
Some people might want to hug it out. Others might not. When I'm triggered I tend to not want anyone but Ogre and a very few select other people to touch me. I get very touch avoidant with anyone I am not one hundred percent comfortable with. My desire to not be hugged (as the triggered person) trumps your desire to hug.
And let's not confuse having a very emotional scene in a game with being triggered. They are two very different things entirely. (I cry easily in games, this is not me being triggered.)
Their boundaries also may include not wanting to talk about it at all. They may just want to play it out.
And if the way they want to play it out is going to trigger or upset you, you do in fact have every right to bow out of said scene. Take a walk and let someone else pilot your character for that scene, get a pop, and have someone give you the high sign for when it's safe to come back.
The resolution of someone else's trigger should not come at the sacrifice of your own mental health.
What else can you do? As with the GM, ask them what they need, if they have not indicated that they do not wish to discuss it further. If it is within your power and you want to, do it. This can be anything from letting their character take point on bloody revenge, to having your character take point on bloody revenge and merely telling them, "It's done."
Honestly, the guidelines for dealing with a triggered person are pretty much the guidelines for dealing with any friend who is having a rough emotional patch, be it a trigger, a death in the family or the loss of a pet. Just listen, and offer help if they want it.
And realize that if you notice someone is triggered before the GM does, it is perfectly ok to call a break, and ask the person in question if they would like the chance to talk to the GM alone, or if they would like you to do it for them.