The most recent Netflix update is enabling picture-in-picture mode for Android 8.1 users. For this to work, you'll two fairly obvious things - the most recent version of Netflix, the update for which has been recently heading out to users, and a device that is running on Android 8.1 Oreo, which you can get from either flashing the developer preview version of the software, or by downloading and installing the beta OTA that Google started pushing out to users just yesterday.
The picture-in-picture mode for Netflix will look just as it does for YouTube, placing a little window on top of other applications. If you've never used picture-in-picture mode before getting it to open up is fairly simple. You first need to open Netflix, then tap on the home button to go back to the home screen. That's it. Once you hit the home button Netflix will minimize to a small picture-in-picture window and put it in the bottom of the right-hand corner of the screen, and from there you can drag the window around to where you want it. You can also open up other applications and the PiP window will stay open and in place until you either close it out or move it to a new location.
PiP mode is part of the Android 8.0 feature list, but even after Google pushed out the final public software for Oreo to devices some apps didn't work and this was cause they didn't support the feature or just didn't work as intended. Netflix was not one of the supported applications. According to Netflix, Android 8.1 Oreo was indeed required for it to enable the feature, although it didn't mention why this is the case. That said, if you're not on Android 8.1 and don't have access to Netflix in PiP model, that's probably ok with you as watching anything in that small of a window may not be as enjoyable as watching something in a fullscreen view. Although there's no word on if Netflix will ever enable PiP for Android 8.0 users, since it's reportedly required that 8.1 be installed, there's a chance that it may very well stay that way. If you're already on Android 8.1, but not the latest version of Netflix, the update should already be live and available for download.