You first need to go to maps.google.com/preview and click "Try Now". Google explains that "the new Google Maps draws you a tailored map for every search and click you make. So whatever you're trying to find or wherever you're trying to go, you'll always have a map highlighting the things that matter most."
So what happens after clicking "Try Now"? You see this message: "Sign in with your Google Account to try the new Google Maps."
While search results are better if you are signed in and you also use Google+, it's strange to see that you need to sign in. After all, the mobile apps for Google Maps work even when you're not signed in.
After signing in, Google shows another message: "Almost there... During this preview, we may email you with product updates or to request your feedback. Please let us know what you think!"
Then you can finally use the new Google Maps.
You can sign out and Google Maps will continue to work.
I hope that the new Google Maps won't require a Google Account (or Google+) when it will replace the existing interface. Just like Google Search, Google Maps works well even when it doesn't return personalized results. Google found a way to personalize search results when you're not logged in, maybe Google Maps will do the same.