It is rather like Azumanga Daioh, but I think it's much much funnier.
Most of the humor is just poking fun at or rambling about day to day stuff, or the occasionally random spazz-out. Things like talking about food for 10 minutes, or making fun of the characters for various reason (Konata, the main character, is a huge anime and video game obsessed geek who'll randomly go off about a game she's been playing or a convention or a new anime, and the rest of the characters will usually just stare at her and be like "I have no clue what you're talking about"
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There's also a lot of very funny one-liners - there's a 'mini-show' at the end called Lucky Channel, and one of the characters is Akira who looks like she's maybe 12. In one of the episodes they were talking about one of the characters of the main show and she comments that "Well, if the maniacs love her I must be a huge hit with the pedophiles". The humor in the show tends to swing from very silly to rather adult and it does so in a split second. There's also TONS of references to other anime, which I've been having fun picking out.
And then probably the best moment so far...the ending sequence of the show is the characters karaoke-ing various songs, mostly anime themes. And I nearly fell off my chair laughing when Konata sang the original theme to Dragonball Z (that goofy "Cha-la, Head Cha-la!" song).
Miyuki sounds kind of weird, but the rest are very good, Konata in particular.
It's great that Lucky Star is being dubbed.
I just had to post this: