If you want to try out the new G+ right now:
1. From the Web interface, go to your Google+ settings (hover over "Home," then select "Settings").
2. Click the button labeled "Manage Google+ activity" (under the "Manage other apps & activity" heading).
3. Click anywhere inside the search bar.
This doesn't permanently switch you over to the new design, but it'll let you use it and navigate all throughout it as long as you remain in that same tab.