John Lawler and others have pretty well nailed it, but I'd just like to add a couple of thing. Maybe if we try and think why it is the present perfect, and the past simple. The past is finished and done with. It doesn't matter how many times you did something or how long you did it for, if you mention a past time reference, or if the fact that something is finished is obvious (eg: Dickens lived in London), use past simple.
Present perfect connects a past event to the present. When I say "I've been to Paris", it doesn't matter when. The fact is I now know what the crowds in the Louvre are like, what the view from the top of Montmartre is, etc; I have this mental picture in my head because I have experienced it. When I experienced it is of little importance. This is John Lawler's existential sense. And when John says "Rebecca has lost her glasses", it means she is without glasses now. When he says "Alexandra has lived in LA since 2000", she still lives there now.
The next thing is time period. When we use finished time periods, such as last year, last week, yesterday, or this morning (if we are in the afternoon or later), we use past simple.
But if we mention a current time period: today, this year, this morning if it's still morning, then we use present perfect. The only exception I can think of is when you come home in the evening, you can use today to mean your working day, then you could say to your partner, "I saw five clients today".
Be careful with the last (or past) year and last year. As soon as we add the, we are talking about the time period specified up until now. So "I saw that film twice last year", but "I have seen that film three times in the last year."
Certain prepositions help: since, over, yet, already (in BrE) and still, are usually used with perfect tenses, not simple tenses. The tricky one is for - "He lived there for ten year", but also "He has lived here for ten years".
Lastly, we often start a conversation with present perfect and then move to past simple when we get down to specifics: "Have you been to Paris?"- "Yes, I went there last year." - "Oh, what was it like?". Or in John's media example, where they use present perfect to give the story immediacy - "The Red Sox have won again! Earlier tonight the Red Sox won a stunning victory against ....", etc.