There are a few ways to greet people over the coming week, but we're going to start with "Shana tovah!"
Here's a great Israeli pronunciation. You'll notice that the accented syllable is different from what many American Jews say: ShaNAH ToVAH. Americans will often pronounce it with an American accent (no big surprise there, I guess): SHAnah TOvah. If you want to hear some American pronunciation (or Lion King pronunciation), the Ramaz School in Manhattan is here to help with a video: How Do You Say Shana Tovah?
And how do you respond if someone else wishes you a Shanah Tovah? You reply the same. Easy peasy.