First of all you need to upgrade to Android 2.2 Froyo. Follow the guide at http://nexus404.com/Blog/2010/05/22/google-nexus-one-android-froyo-official-installation-instructions-android-froyo-almost-ready-for-your-nexus-one-you-can-install-it-alone-here’s-how/.
Next, you would think Flash was installed out of the box. It is not. To install it go to the Market, search for flash and select "Flash Player 10.1 BETA" (with an Adobe 'f' icon). Install this. Now you should be able to view flash content in your browser.
Solution found at: http://www.sizzledcore.com/2010/05/23/flash-player-10-1-beta-for-android-2-2/