I know there has been much commenting on the Virgil version, but seeing as I'm teaching it next year I thought I'd do the narrative account thing for practice. The first paragraph following is general backstory that Virgil doesnt give, and the second is the blow-by-blow account according to Virgil.
Firstly, back story to the Aeneid. Dido is the sister of evil Pygmalion and had to flee from him. She was married to Sycchaeus, whom she loved very much and because she loved him so much didn't want to marry again - it's not so much that remarrying was looked down on in Virgil's Rome, indeed it was very common among the nobility because the men used to go and get killed in wars all the time (think of Cornelia wife of Crassus and Pompey), but the main point is that she loved Sycchaeus so much.
The Aeneid opens with Aeneas in a storm, and he ends up washing up in Carthage. His mother, Venus, visits him but pretends to be a young hunteress type, which annoys him when he realises it was her. When Aeneas gets to Carthage, he see the temple they're building with all the scenes from the Trojan War and starts crying, at which point Dido notices him and invites him to dinner. Venus replaces Aeneas' real son, Ascanius/Iulus with her own son, Cupid, and Dido thinks he's lovely and has him on her lap all night - in fact, Venus has decided Aeneas will be safer if Dido falls in love with him (Venus is a silly girly sort of goddess whose main traits involve making sure Aeneas is safe and lying a lot), and this is what she is making happen. At dinner, Aeneas is persuaded to tell his story, Odysseus-style, and so he launches into a two-book-long narrative of a) the Trojan War (when he was given his mission to go and found a new Troy that's going to turn out to be Rome in the end), and b) his adventures on the journey from Troy to Carthage (involving Harpies and things). In Book IV we get all the lovey dovey stuff - they go hunting, it rains, Aeneas and Dido go and have sex in a cave and then spend quite a while sleeping together. Dido is smitten and thinking of herself as wifey, but suddenly Aeneas gets a message from Mercury that he really should be getting on with his quest, and because his main trait is piety he has to go along with this. There is a very interesting exchange between him and Dido in which he says he has to leave, she cries, he says he really does love her, she cries, he leaves, she cries, she's not-comforted by her sister, she builds a big pyre and jumps on top of it and kills herself. Iris (random deity, not important) takes pity on her and cuts the threads that tie her to life, so that she can die properly and her soul can pass on (suicide is complicated, you see). Aeneas forgets about her for a while but when he gets to Italy ends up going to the Underworld, where he meets her soul - she ignores him, he cries after her. But it turns out she's now with Sycchaeus, which is rather sweet. But it's all a bit complicated and bound up with eschatology - I wrote a whole thesis about the life cycle in the Aeneid, so believe me there's no easy answer to the suicide and morality question ;)
Um, did that help? Hope so!