Siri's problem is probably with pronunciation, at least as far as your contacts go. if you say, for example, "Siri, call Friedrich," and she says, "i can't find a contact named Frederick", you can say, "that's not how you pronounce Friedrich", and she'll say, "okay, how do you pronounce the name?" and play her beep-cue for you to say the name. you say the name, and then she'll take you through a process-of-elimination thing where she says the name a few different ways and you pick which one is the closest to correct. she should recognize the name from then on.
teaching her words in general, though, i don't know about - i just came here looking for the answer to the same question. she doesn't know the word "gist" and insists that i'm saying "just". what you say to Siri appears at the top of your screen (we're talking about Siri here, as such, and not about voice recognition - speech-to-text, like you're using when you dictate a text message) and you're supposed to be able to correct her by tapping the text of what you said and editing it; this is supposed to make her understand what you say better, but it's not working for me and "gist." i've corrected her about four times and she just keeps on hearing "just". i'm gonna keep looking for an answer.