To be fair, some of the action in this story appears in dialogue. For example, Gandalf explains his battle with the Balrog in his own words, and Merry relates the destruction of Isengard directly to his friends.
But for the most part, we get the facts from an omniscient, unnamed narrator, thanks to his ability to roam around Middle-earth with fleet feet. Let's face it: our narrator is a huge know-it-all, and while this might annoy us on any given day, when we're reading The Two Towers, we're quite grateful that he's such a big nerd. For one thing, it gives us (fictional) historical insight on the current events of Middle-Earth. And for another, if you think about it, only an omniscient narrator would be able to unite the different narrative strands of Aragorn, Gimli and Legolas; Merry and Pippin; and Frodo and Sam with a consistent tone and style.