Based on what Google has shared on its blogs and elsewhere, the "priority inbox" system is being rolled out on a server-by-server basis, which means that some people see it before others do. When it finally became available on my own Gmail account, I enabled it to see how it works, but frankly am not hugely impressed.

Still, you asked how to try it, so let's start there.

I logged in to my Gmail account and along the top was a highly visible red link:

That's easy enough! I clicked on "New! Priority Inbox!" and a window popped up, with an embedded video:

Yeah, whatever. I just wanted to enable priority inbox, so I clicked on "Try it now!" and was promptly shown a starting configuration window:

Looks like one of the messages has been incorrectly categorized as unimportant. To fix it, I'll click on the tiny yellow "+" symbol, as highlighted with the tooltip:

That looks right, so I click on "That looks right" and...

*poof* I have the priority inbox enabled in my Gmail mailbox:

Since I don't use stars to highlight specific messages, that section is empty, but it's easy to hide it, as shown. There's more you can do to tweak these settings too, as shown with the pop-up menu associated with "Everything else":

At this point, I'll try using the priority inbox service, but since I already triage my email as it arrives and have over 30 rules organizing mailing list related messages into labelled photos, I have a sneaking feeling it's not going to be particularly interesting or helpful for me.