I suspect it depends on where you are....if it's the UK there aren't many things that will kill you quickly enough that you can't get to decent medical aid.
Take a bit of the plant with you, ID is crucial.
If it's an allergic reaction take antihistamine, quickly. That's all they'll give you at hospital for it anyway, and only if you don't respond will they administer the equivalent of an epi pen.
None of our plants will kill you instantly. Some will leave you greatly debilitated with nausea and diarrhoea, some will cramp you up to tears. The worst ones will slowly kill your liver.
If you have eaten something toxic, wash out your mouth and spit, wash and spit and dry off your lips carefully. Vomiting; usually that'll just add acid burning to the throat and mouth. Get to a hospital asap.
Particularly if it's a fungal poison, or hemlock water dropwort.
If the body can be supported through the effects of the poisoning then it can recover, but if the poison affects the muscles, such as the heart and breathing reflex, then without assistance you're unlikely to survive.
Straightforward first aid advice :-
http://www.sja.org.uk/sja/first-aid-advice/poisoning/poisonous-plants-and-fungi.aspx
Bear in mind that a great many plants are mildly not good for us, the little oxalis for instance, but we can eat 'some' with no ill effects. I can eat elderberries with no problems, but not everyone can. Keep it relevant.
If it's a child, don't hesitate, get medical help asap. Things like laburnum seeds can be incredibly dangerous for them.
cheers,
Toddy
p.s. didn't mean to contadict JohnC
Vomiting is generally a bad idea, but tbh if I've eaten something dodgy I do it. I just don't advise it iimmc.