The first important thing to know about Virgil's writing style is that he wrote in metrical verse – specifically, in the meter known as "dactylic hexameter," which you can learn more about here.
Virgil's writing is also characterized by a very precise attention to each individual word and the shadings of meaning it conveys. Often, these shadings of meaning arise from connections with other literary works, especially Homer's Iliad and Odyssey, though these connections are not always straightforward. Sometimes, Virgil can torque a reference to Homer to get a different point across, as when he borrows the idea of announcing the subject of his poem in its first line; instead of asking the Muse for inspiration, he says he's going to do the singing himself: "Arms and the man I sing." (For a fuller discussion of this line, look at our section on "Allusions.")
Additionally, Virgil's writing displays a highly visual imagination, which can be seen, for example, in his vivid depiction of the fall of Troy, which is much more terrifying than your standard disaster movie. The visual and intellectual aspects of Virgil's poetry are always complemented by a very close attention to the sound of his lines – though unfortunately this does not come across in translation. To get a sense of how Virgil sounds in Latin, check out the relevant Audio and Video links from our "Best of the Web" section.