In its "Guidelines for Webmasters" document Google notes that "search engine spiders see your site much as Lynx would".
A web spider is a program that searches through the internet for content (see here for more definitions.)
Lynx is a web browser that was used in the good old days of internet before we had fancy things like mouses, graphics, or sliced bread. Put very simply Lynx is a bareboned web browser that supports a minimal set of features. You can download a free copy from this website. There are other uses for Lynx other than SEO (such as pinging a webpage in a crontab), but for SEO it is mainly used for usability and visibility testing.
If you don't feel like installing new software there are a number of online spider emulators that will try to show you how a spider views your website. One that I found is available here.
Now that we have the means to see how Google spiders view our website we can have a look at what implications the guideline has for our site.
Firstly we need to realize that search spiders "crawl" through your site by following links. Obviously if a spider is unable to read a link then it won't find the page the link points to.
Google maintains an easy-to-read list of technologies that it supports. You can find it online here.
View your site in a spider emulator or Lynx and make sure that you can navigate through the links. If you can't then there is a good chance that Google can't either.
One way to nudge spiders along is to provide a sitemap. This also helps your human readers. Remember that Google does not like you to have more than 100 links on a page so if you have a large site try to identify key pages rather than providing an exhaustive list.
Some people argue that if you need a sitemap then your navigation system is flawed. Think about it - if your user can't get to content quickly through your navigation system then how good is your site at providing meaningful content? Personally I like to balance this out and provide sitemaps as an additional "bonus" while still ensuring that all my content is within 2 clicks of the landing page.