Yesterday I wrote: "social skills don't convince anybody to do anything; they direct people's attention towards or away from facts, predictions, or lies that will appeal to the listener." What I'm getting at is that it's the content of what a person says that persuades a person. I want to give a couple examples, starting with something absurdly basic: getting a swordsman to join your adventuring party.
The modern way to handle this is through social skills, something like Bargaining skill if you offer the swordsman pay, Intimidation if you try to coerce him, Guile or Acting if you lie to him and claim to be working for someone he knows and respects. But really, it should be what you offer, what threat you make, what lie you use that persuades. In real life, a person who knows how to bargain knows what the fair price would be for various personality types; a person who knows how to intimidate likewise knows what threats might work for which people. If you're going to use skill rolls, social skills should be used to provide clues to what offers or threats to make, instead of as a technique for taking over an NPC.
So take our swordsman. We want him to join our party and attack an ogre tribe. Does this idea frighten the swordsman? Then mentioning it is likely to get a negative reaction. Does he have a beef with the ogres, but can't find other people to help take them on? He's likely to jump at the offer. Do you offer him gold? If so, how much money would he expect? Is he greedy, demanding more than the going rate? Has he heard of you, and if so, how does he feel about you? Do you have a reputation as someone who hires people who are never seen again?
For every simple request, there are specific things you can mention that will increase the chances of an NPC agreeing, and specific things that will make an NPC reject your request. Most of the time, you won't have personality information relevant to what the PCs are asking, but that's OK; that's what you have a reaction roll for, to decide how an NPC feels. Most reaction roll mechanics are elaborations of a 50-50 roll, with adjustments for dangerous versus trivial requests. Some requests, like "kill yourself", will almost always be rejected, and others, like buying a simple item from a merchant who sells that item, are almost always accepted. For such requests, there's no need to roll. For others, make a quick roll and modify it from whatever prepared or improvised personality information you have on the NPC. Judge the content of what players say by picking out key words and the players' apparent attitude towards those concepts. Are they insulting the king? Then you have to decide what the general local feelings towards the king are, or whether the NPC's particular demographic feels differently than the masses. If you actually wrote notes on an NPC, you might already know that the NPC is a rebel, or a loyalist. And as you make reaction rolls, some results may be highly unlikely, but show up anyways; you can take these to indicate unique personality features, which you can then add to your notes, building the NPC's character on the fly.
This should pretty well cover simple requests, but what about extended persuasive conversations, like debates before a jury? I'll cover those in a future post.