How can I get replacement stickers for a new lego set?
LEGO Customer Service will be probably be happy to help you out. They've been happy to replace missing or broken parts for me in the past. They have an online service for requesting replacement parts here:

https://wwwsecure.lego.com/en-us/service/replacementparts

I don't think sticker sheets are listed in the inventories on that page though, so you'll have to add it manually using the "I can't find what I'm looking for" link at the bottom. Once the sheet is added to your cart, you just need to checkout and provide an address for shipping purposes.

If you have any problems, you can also contact customer service directly from this page:

https://wwwsecure.lego.com/service/contactus/