"People" and "persons" are both technically correct, but you will usually only ever read "persons" in very specific contexts. I don't think I've ever said or written "persons" in my entire life. You commonly see it in legal contexts, but otherwise it's rarely used ex. "Police are currently searching for missing the persons", "This elevator can hold a maximum of ten persons", "This product is not suitable for persons under eighteen years of age" etc. Sadly, I've even heard native speakers more than once say "Hey, they spelled 'people' wrong!". That's how uncommon it is. It's good to recognise "persons" when you see it, but you will never go wrong if you always say "people".

I've heard "persons" in American English, but as: "American" - in this case - is a synonym for "incorrect", go with "people" for everyday usage :D I remembered a scene from: "Taxi Driver" where one of the drivers tries to sell a piece of "Errol Flynn's bathtub". He said you could: "see the watermark of three persons".

"two people" There are a few occasions where one might use "two persons" but their almost exclusively in journalism or legal cases. You'll almost never see it in daily reading.

Your first choice when talking about more than one person is "(two) people". "Persons" only makes sense if you mean "individuals"... and as 郭东兴 has pointed out, this is quite uncommon.

Persons is an old word, from formal English. For instance, I've heard on trial: murdered by person or persons unknown. --> Legal language is often more formal and traditional than daily chatting. Furthermore, you will find that word throughout the literature of the XVIII and XIX centuries in classic authors such as Jane Austen or Charles Dickens. This word was also used by totalitarian regimes to give a flavour of tradition, for example, by the segregationist South Africa, in banners and documents: http://upload.wikimedia.org/wikipedia/commons/1/12/ApartheidSignEnglishAfrikaans.jpg Anyway, I was told not to use this plural form any more. I hope this helps you.