The first thing you need to do is cease the currently failed backup attempt:
• Open System Preferences from the Apple menu and click "Time Machine"
• Click the (x) icon on the right side of the progress bar to stop the backup attempt
When the progress bar disappears and it no longer says "Preparing backup…" you're good to begin the troubleshooting process.
• Open the Time Machine drive in the Finder and navigate to the "Backups.backupd" folder
• Open the folder within Backups.backupd that is the name of the current Mac which is stuck on preparing
• Put this directory into "List View" and sort by ‘Date Modified', or just search the folder for a file with a ".inProgress" file extension
• Delete the "xxxx-xx-xx-xxxxxx.inProgress" file. The .inProgress file is always in the form of xxxx-xx-xx-xxxxxx.inProgress, where the first 8 digits are the year-month-day (date) and the next 6 or so digits are random numbers, followed by the inProgress file extension.
• Restart your Mac
• Once rebooted, let Spotlight run completely (you can either just wait it out or watch the mdworker, mrs, and related processes in Activity Monitor). This should cause macOS to re-index the attached Time Machine drive if it's needed, which may be getting in the way of Time Machine backing up properly thus causing the computer to get stuck on "Preparing backup..." for a very long time.
• Start a back up yourself. Pull down the Time Machine icon and choose "Back Up Now". You will still see a "Preparing backup…" message but it should be gone within a few minutes, depending on the size of the hard drive, the speed of the Mac, and the size of the backup to be made. At this point, your Time Machine backup will proceed as expected, so just let it run and you're good to go again.