Speech is used for many things, such as diplomacy, intimidation, gathering information, and improving disposition.
Disposition is how much the NPC trusts your character. If they don't trust you, they would react differently in plain conversation than if they did trust you. They might not even be very fun to be around, since their sense of humor or politeness, or tenacity, or whatever, won't show until their disposition is at a certain point towards you.
Different NPCs have different degrees of trust, determined by the GM - some, such as tough wastelander mercenaries, are wary to trust anyone, hence they only trust you when their disposition is very high. If they do trust you however, chances are they will fully trust you, because it is required of them through their contractual binding. Other NPCs hand out levels of trust in bunches, such as matronly homemaking characters that love to spread gossip. Other NPCs still are very easy to convince, ie. children or the foolish.
There's always a trick to get an NPC to trust a player, but this can only be found through roleplaying.
There are also other ways, but the player must go with the assumption that the NPC is willing.
Simply introducing yourself opens up the chance for the NPC to use their empathy on you. If they learn enough about you, they may decide to trust you some more. This is disproportionate to their disposition that they already have towards you - if they think your disposition is already very high and their disposition to you is low, ie., then their disposition might go up a fair bit towards you.
Revealing something about yourself.
Chatting them up. When chatting up an NPC, there's a static DC that applies to each conversational action. There are plenty of general actions that can be done in vague meaningless small/trash talk.
Assuming the NPC even has the time to chat, these actions are:
- Tell a joke. A joke tends to lighten the mood, but doesn't open up the chance for any empathy apart from 'he found this funny'. If an NPC absolutely hates the joke, it will only foul the mood a bit and their disposition lowers only slightly (unless you offended some core belief they had, or their mother, or their home, etc.).
- Boast. Some NPCs like to hear of your achievements, so that they can compare their strengths/weaknesses to your own. Others that think they're already strong enough themselves, get sick and tired of it. You must compare your self control to their empathy to ensure that you don't reveal too much about yourself accidentally.
- Admire. Some NPCs like to be admired. Others get sick and tired of suck ups. Admiration tends to paint you as weak.
There are other actions too. However, they must be applied to the conversation 'wheel'. The rule is that four different actions must be successfully completed in tandem in order to have any chance of effecting a new raised or lowered disposition - note that each rolled action (your speech skill) might effect disposition anyway based on success or failure (GM discretion). The wheel has a number for the intensity of the effect the action might have over the NPC - ie. with a very intense joke, the joke might be considered very funny or be very rude, depending on the NPC.
If you're speech skill is high enough, you can take advantage of perks to effect the wheel in different ways - rotating one notch will give you the opportunity to turn a weak action into a more intense one, ie.
Making the wheel is simple - just paper and pencil. Alternatively, it can be constructed in paint - however, it should be legible and the pieces should be separated in a program such as paint.net for rotational ease. Each time the PC chooses an action from the wheel, that action darkens and cannot be accessed until the next 'go'. Each go is four actions and randomizes or swings depending on the over all nature of the conversation (roleplaying; when roleplaying however, each go must remain on-topic, or the wheel resets and there may or may not be disposition loss). At very high speech, the PC can customize their wheel with actions other than 'boast', 'joke', etc.
Coercion is the most roleplaying intensive thing. If it fails right off the bat, the NPC will trust you a lot less. If it succeeds, then the NPC trusts you a bit more, and additionally, they will believe whatever you said during your use of coercion. Coercion is an action that must be invested with your speech skill's social points (social points are equal to percentage in speech * competence rank). Increasing coercion by a rank is equal in cost of social points to the next rank to be purchased - so, ie., if you want to increase coercion to rank 3, then it will cost 3 social points.
Coercion requires a lot of empathy - you must know the NPC's personality to know what they want out of life. A GM can find several ways to quickly describe a PC's personality - they could use D&D's alignment for generally accurate estimates, MTG 'colours' for more accurate estimates, and paragraphs for the most accurate, etc. Of course, knowing personality is different than knowing an NPC's past - to know the past, a player must ask questions and then roll their sense motive to set a DC versus any attempts at lying.
Seduction and Sex
It always depends on the NPC, but many NPCs must have a certain amount of disposition towards you before anything sexual happens between you. Also, they must swing that way!
Seduction requires a great deal of care. But it's easier than some things - after all, it's simply a proposition. If you succeed at seduction (appropriate roleplaying + speech save vs. mistakes and attempts at rejection), you may engage in the act of sex with the NPC - just choose a time and a place.
What is Sex in this Game?
Sex swiftly heals stress damage, and it is also a great way of really enhancing an NPC's disposition towards you. It's also probably the most powerful tool that can be used for the greater scheme of coercion. If you do the sex too many times in a single day though, you may actually take stress damage instead.
Some NPCs are affected by sex more than others - a tough wastelander mercenary doesn't let sex get in the way of more important thoughts, while a naive vault dweller might crusade entirely in the name of sex with a hot girl.