To take a screenshot on Nexus and Pixel phones, you'd use the power + volume down button combo. For a brief moment, you could even use Google Now on Tap to take screenshots without those hardware buttons, but Google Assistant eventually removed the functionality. Now, easier screenshots are back with Android P.
Yes, you can still use the power + volume down button combination to take a screenshot like you normally would in stock Android, but it seems way slower than it should be and, if you're like me, isn't easy to trigger every single time. Thankfully, in the new Android P developer preview, all you have to do is open the power menu and tap "Screenshot." Yep, it's that easy.
To explain in a little more detail, press and hold the power button until the power menu pops up, then tap the "Screenshot" option. When you do, the power menu will disappear and the screenshot will be taken. Afterward, you'll get the "Screenshot saved" notification as normal which now includes an option to "Edit" the screenshot right away.
So, while Google replaced the Google Now software shortcut for screenshots with the Google Assistant, they included a similar shortcut feature in Android P to fill the hole, and I've got to tell you ... I'm never using the power + volume button shortcut again (unless it's to take a screenshot of the actual power menu, of course).