Because I always do, let’s start with the story. At the outset of the game, Peach finds herself captured by Bowser once again, and before you even have time to wonder who actually governs the Mushroom Kingdom most of the time, you’re blasted onto a tiny planet by a Magikoopa. After some tutorials, you’re introduced to Rosalina, who oversees the Comet Observatory with a bunch of star-shaped creatures called Lumas. Her Power Stars have been taken by Bowser, and you need to collect enough of them to get the Observatory up and running again, so you can get to Bowser and rescue Peach. There’s also a bit of an optional sidestory going on featuring Rosalina and the Lumas, which you can explore at your leisure; I recommend doing so unless you don’t feel like becoming depressed, because that story is fairly depressing.
The story’s pretty simple, but it does its job, which is to provide some exposition onto why you’re in space and then never interfere again. The few times it does come into play (essentially the beginning and end of the game), it’s done through very nicely done cutscenes, which apparently take some pointers from Twilight Princess in the high level of quality cinematography. The voice acting is highly limited; Bowser makes growling sounds, and there are some snippets here and there from the main characters. Others have complained about the lack of full voice acting, but I have always had an aversion to it being in big-name Nintendo titles like Mario and Zelda. There are definitely games that are intended to have full voice acting; Metal Gear Solid is one of them, Galaxy is not.