Google's Pixel phone launched without any sort of feature to make notifications quickly viewable on a locked device. In order to view an alert, you had to pick up the phone and press the power button or touch the fingerprint sensor.
In early December, Google released a software update for the Pixel that adds two important, and much missed, features: Lift to wake and Double-tap to wake. However, you won't find any mention of the features in the change log.
Update your Pixel if you haven't already by going to Settings > About phone > System updates > Check now. Full instructions covering the update process are here.
With the update installed, go to Settings > Moves, then scroll to the bottom of the page.
Tap on the phone icon next to each respective feature to see a quick demo showing how to use each feature. Slide the toggle switch to the On position for one or both of the new features. Should you later decide you don't like one or both of the features, go back into Settings > Moves and turn them off.