Where to Start When You've Broken Your Android Phone Screen? Here's a number of strategies you can try.

There's a great number of ways to interact with a phone but being able to see what it's displaying is probably the most important.  Unfortunately, smashing a screen is an all too common occurrence and with the poor state of voice assistance, and strengthened security across Android, it's become harder to get into a phone that's been smashed.  Although the regular backup system with Google Cloud and other apps with backup capabilities has improved, sometimes you just really want to get back onto that phone to rescue data.

Listed below are a number of strategies you can try to gain increased access to your broken phone. Immediately assess whether or not your phone has some life left in the screen and digitizer.  If the digitizer still works, even partially it will be helpful.  If the LCD/AMOLEDs are bleeding purple or black, you'll have a limited time before the screen completely fails... so best to enable some of the remote control options (6, 7, or 10) below.

1. If your phone has MHL capable USB-C port or a Micro-HDMI port, then you could get a cable and output to a monitor or TV.  Some phones have DisplayPort Alt Mode which works like Apple MacBooks and allows the use of a USB-C hub with DVI ports, DisplayPort, or HDMI port. (https://www.quora.com/Can-I-hook-up-my-USB-type-C-phone-to-my-monitor-using-a-USB-C-to-VGA-adapter)
2. If your phone is not capable of the above, you might try other tech like a DisplayLink dock (https://forum.xda-developers.com/oneplus-5/themes/wired-tv-one-plus-5-makes-displaylink-t3667974, https://www.youtube.com/watch?v=QXhPvW-aOtY) or dongles like Chromecast and Miracast.  Keep in mind, most of these require a step or two of setup on the phone, so it would be tough to know where to press if your screen is broken.
3. If you have a good idea of where to press and what dialog boxes will pop-up on the phone, then you might be able to use your fingers or a mouse connected via a USB host dongle.  I used a USB-C to USB-A female cable to allow mouse input.
1. If you're lucky and have access to another identical phone with the same version of Android, then figuring out where to press will be easier.
2. YouTube videos and screenshots will be helpful.
3. Tactile feedback and click tones being enabled will assist with navigating blindly.
4. If your digitizer is also broken and don't have a USB adapter, try a finding a compatible bluetooth mouse. My Surface Arc Touch mouse didn't work.  Might be necessary for unlocking the phone since fingerprint authentication doesn't last forever.
4. Use voice control "Ok Google" Open Display Settings, etc. You'll need to be connected to the internet for this...
5. Enable Google TalkBack.  I was unsuccessful enabling this feature blindly, but it would've been a huge step in the right direction.
6. Connect your phone to your PC and use adb commands from your PC. 
1. Or, provided you're rooted, use adb from Terminal Emulator on the broken phone using a physical keyboard attached via USB.
7. Remotely install apps like Screen Mirror (https://play.google.com/store/apps/details?id=com.ajungg.screenmirror) (alternatively: https://play.google.com/store/apps/details?id=com.livescreenapp.free) from Google Play via your PC.  This is the solution that ultimately worked for me because it required very few screen presses to enable and I was logged into my private WiFi network already.  Just a fantastic app!
8. From step 7, I was able to copy over an adb_keys file that was authorized with the adb installation on my PC.  I needed to place the adb_keys files in /data/misc/adb to allow adb to work with the broken device, otherwise the adbd server kept saying $ADB_VENDOR_KEYS is not set.  This allows USB debugging with my PC (I already enabled USB debugging mode long ago).  Since I was rooted, it was simple for me to place the file in that directory, otherwise it might be possible to do it via adb while in Recovery mode. (Boot to recovery with phone-specific key combination)
9. I was able to get Vysor (alternatively: scrcpy) working which has a very simple setup and automatically installs Vysor to the phone via the desktop app, but requires that USB debugging (Step 8) is allowed.
10. I also enabled WiFi Direct/Miracast screen mirroring on the phone and my Windows 10 laptop as a back-up measure.  This may be the best tactic to try if you know where to press, since it's at the bottom of the Display settings in most versions of Android... just hope you don't have too many neighbours with Miracast capable devices.

Other strategies and tools in links:

https://forum.xda-developers.com/showthread.php?t=2588979 (ADB and fastboot together)

https://stackoverflow.com/questions/29072501/how-to-unlock-android-phone-through-adb

https://www.xda-developers.com/adb-tools-adb-over-wifi/

https://android.stackexchange.com/questions/142533/run-adb-command-inside-the-terminal-emulator-or-programmatically-without-root

https://github.com/jackpal/Android-Terminal-Emulator/wiki/Android-Shell-Command-Reference

https://stackoverflow.com/questions/10506591/turning-airplane-mode-on-via-adb

https://www.theandroidsoul.com/change-remove-lockscreen-pattern-pin-password-adb-android-oreo/

Pre-emptive measures, in case you smash your phone.

Enable USB debugging mode through developer options (tap build number 7 times to enable dev. options)

Install Screen Mirror app
Install Airdroid app
Get a Roku with the Roku screen casting app.
Get Chromecast (limited mirroring capability)

Root your phone, though there are drawbacks to this. Some phones can not be rooted.  Once rooted, install Terminal Emulator.
Bootloader unlock your phone, also drawbacks to this. Most phones can not be bootloader unlocked.

Setup Vysor (PC and on phone) which will ask to authorize USB debugging mode and create an adb_keys file on your phone. Backup the set of files created when first allowing USB debugging when Vysor makes the confirmation pop-up: adb_keys (on phone) and adbkey.pub, adbkey (on PC)

Setup screen casting (place check in tick box Enable wireless display from Display -> Cast settings) to project to your Windows PC.  I believe this is Wi-Fi Direct/Miracast technology that is supported in Windows 10 on modern wireless chips through the "Projecting to this PC" settings.  This is called Screen Mirroring on Samsung phones.

Set default Media Transfer Protocol (MTP) mode when USB cable connected.

Memorize and/or screenshot the positions of toggle buttons when two-finger pull down the notification shade.

Don't encrypt your phone.