Turns out, you may already have the assistant. Make sure you've got voice recognition turned on, and your phone responds to your saying "OK Google." I was getting a notification in Settings to record my voice, which I'd already done, but I guess it got canceled somehow. At any rate, after I recorded my voice again and tried it out on my Nexus 6, up popped the Assistant. None of the snazzy home button animations or anything, but it took down a reminder for me and answered a few dumb questions.
For now, on my phone, the assistant still seems to be tethered to Screen search. Long-pressing the Home button still only brings up Screen search options; the assistant only arrives in response to an "OK Google." I don't know if this is a Nexus 6 limitation or just a halfway point in prepping for the actual update.
[PS] The reminder--to buy Advil when I was at a specific supermarket--worked.