My current understanding of the plot is behind this LJ cut. However, I have a few questions, and enlightening answers to them would be really appreciated. I did read the wikipaedia article, but it wasn't much use.
Dido and Aeneas
Belinda: Life is great, we're pretty and powerful, and should be happy all the time
Dido: I don't want you to guess why I'm unhappy. I can't tell you why I'm so unhappy. Repeat several times
Belinda: I know why you're unhappy. You fancy Aeneas. But that's a really good thing as it'll unite our cities. Besides, it's OK, because he fancies you too. Oh, here he is.
Aeneas : Hi
Dido: Fate forbids what you pursue 
Aeneas: Dido, I love you. Have some pity on me!
Belinda: Oh, come on, it's obvious she fancies you too.
Chorus: Yay! Let's all go and party! 
Sorceress: Mwahahahaha! I hate Dido because I hate everyone who's better off than me! I will cause terrible things to happen to her!
Witches: Hahahahahah! Tell us how! 
Sorceress: I'm going to get my elf to pretend to be a God, and tell Aeneas that he has to go away!
Sorceress: Oh, and I'm going to spoil their party by raining on them.
Belinda: Yay, what a great party!
Aeneas: Look, look, I've got a really big pig on a stick!
Dido: Damn, it's going to rain. Let's go home.
Aeneas: Better do what God says then. Bother. Dido's going to be a bit upset about this.
Saliors: We're sailing soon!
Witches: We're really evil. We're going to storm them as soon as they're at sea. Yay! Elissa bleeds tonight and Carthage flames tomorrow!  Mwahahahaha!
Dido: My only refuge is Death! 
Aeneas: I'm really sorry. It's God's fault.
Dido: Hah! People always blame God when they're doing bad stuff. Go away and let me die in peace 
Aeneas: No! Tell you what, I'll ignore God and stay with you for love's sake.
Dido : Humph. I'm not going to forgive you just because you stay. You said you were going to leave me. That's just as bad.
Aeneas: I'll stay!
Dido: Go away.
Aeneas : I'll stay!
Dido: Go away! I'll die if you don't go away! 
Aeneas gives up
Dido: I'll die now.
Dido dies 
 Why? Is her loving Aeneas a bad thing in some way?
 Why does Dido think Aeneas is fated not to get together with her? I feel I'm missing some back story.
 Did I miss something here? I didn't hear Dido say yes!
 No questions here. This bit's great
 Yep, definitely missing some back story. What's Troy got to do with this? I wish I'd done classics.
 Who / what is Elissa?
 That's here, right? Dido is the Queen of Carthage? I still can't see why the city's going to spontaniously combust... Or does it mean that they're going to burn the Queen in her funeral pyre?
 Now I'm really confused. This seems a bit of an overreaction to some guy she only told she fancied yesterday vanishing. Is this an opera thing?
 I still don't get why she's going to die. Death of a broken heart might be a good plot device, but even Juliet used a dagger.
 If she's going to die if he doesn't stay, surely this doesn't actually matter?
 I mean, is it that there's some crucial stage direction involving poison or a dagger or something I'm missing, or was the style of the day that people really did just drop down dead of broken hearts?