Old site search engine result -> New site

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I am updating my workplace's existing site. When you type in "vegetarian chicago" it is one of the top listings in Google. http://www.veggiediner.com The site was set up by someone else years ago, and I'm not familiar with the techniques for making pages/websites search engine friendly.

I was wondering how I might replace the old site with the new WP site when it is ready http://www.veggiediner.com/wp while possibly maintaining the same recognition in Google? I don't want to throw it all away and start from zero, if at all possible.

Any suggestions or referrals as to how to address this? Thanks!