Now it's much easier to get ahold of a browser with the Dart VM. If you're using Linux or Mac OS X, you can download Dartium today. Windows builds are not available yet, but should be available "soon."
Google does warn that Dartium "should not be used for day-to-day browsing" but says that the Dart VM integration will come to Chrome "after more testing and developer feedback."
If you're interested in trying out Dart and Dartium, be sure to read over the intro and language basics pages. The language basics page also has an embedded app to run Dart code directly in the browser. You can also grab the Dart Editor for Linux Windows or Mac OS X.