Using your browser, navigate to http://archive.org.
I decided to check out Amazon's humble roots since I've been reading the Jeff Bezos biography One Click.
The Archive.org meta crawler visits popular sites more often. Each blue circular bubble indicates that a snapshot exists. In my case I searched for Amazon, the 7th most popular site on the web; this explains the blue blur that you see below.
You might notice by the "annual" snapshot bar graphs that overall snapshots have increased over the years -- this is due to hard drive space becoming less expensive, resulting in more crawls being possible. After all, each snapshot isn't just a mere image -- it's an explorable version of the site.
From here, you can either select a blue bubble to view the relevant snapshot or choose a different year to view. Let's go deeper. Select an older year.
After you've selected the year, find the specific date you'd like to explore. Explorable dates are denoted by the blue bubble. A larger bubble means that multiple snapshots exist for that date. Click on a date bubble.
It's interesting to see not only how web design has changed but also how far we've come in such a short period of time.
Amazon in 1996: See it in action