The search engines each have their own software program that "crawls" the internet simply by following one link to another from one website to another. Search engines like following links because it's what they're best at. Hyperlinking from one website to another is what made the world wide web happen, and search engines still follow hyperlinks as their core method to find new information.
Some things to watch out for:
1. Don't use CSS for linking from your navigation menus. Make sure your navigation links are using the traditional <a> HTML tag for linking to your pages.
Other things to watch out for during the (re)design of your website include a few technical aspects that can ruin your day. Here are a few:
1. Make sure the robots.txt file on your site doesn't limit access to important pages within your site. Web programmers will often times try to tweak the robots.txt file to improve the speed at which a search engine will crawl your site, but sometimes those tweaks backfire.
3. What happens when your website returns a "404 error page?" You need to set your website up so it will show users some default message when they request a page that doesn't exist, or broke. You might not realize it, but this happens all the time. You should consider updating your 404 page often to include some type of "that didn't work message" followed up by a "take a look at our current specials or events instead."
Using these 6 items to help guide your website design and functionality will increase the potential that the search engines spider and index your website more accurately.