Step #1: Make sure you dominate rankings on "the Googles" for every conceivable way someone with half an ear on the television could mangle your name or category. She isn't going to product.com, she is googling for [product], [product.com], [products], [praduct], [pro ducks], [what was that thing on Oprah this morning?], etc.
Step #2: Expect less traffic than you think, because while Oprah's audience is ginormous they are in TV watching mode rather than browsing the Internet mode, and large portions are going to fall out of the funnel in a) trying to go to your website and b) doing so successfully. Oprah's peak audience is somewhere around 9 million people. If you're expecting 500k visitors to your website, I think you're being overly optimistic (absent Oprah literally doing a call to action on your behalf). So it isn't all that much worse than a Slashdotting, and you can expect the people to come in over a wider interval than "right the second the URL appears on the screen". Any reasonable website can chew through 500,000 visits spread over a 48 hour interval if it survives the initial bump.
Step #3: Scale the obvious bottlenecks and get ready to do some firefighting, though you probably won't need to. If the home page makes 10 SQL queries right now, a) fix and b) replace with static HTML for the day (or get a process in place where you can do that quickly if the server starts to chug). I'd put a big Welcome Oprah Viewers banner at the top of it with a sales pitch leveraging that social proof for all you are worth and giving them "special" advice for using the site, by the way.
Step #4: Have a backup plan. If it seems highly unlikely that you're going to survive, switch all or most users to a static site which explains that "due to overwhelming popularity" the service isn't available at the moment but you'll email them the second it comes back up if they just drop their email address into this MailChimp signup form. Do so. Give them an option from hearing from you in a less transient fashion, too. (I would strongly consider "Check if they're cookied for your site, if so let them in, if not give them the static pseudo-site" but that doesn't scale to the moon like "hello new client, here is index.html, bye" does.)