OK – launch TextEdit (via Spotlight), and hit Shift-Cmd-T to switch to plain text mode (as opposed to rich text).
Now copy and paste the following three lines:
#!/bin/bash
killall NotificationCenter
osascript -e 'display notification "Notifications" with title "Fixed"'
(The 1st line selects the command line interpreter, which might not be necessary for a .command file, but in case you'd like to run it from the terminal. The 2nd line does the magic. The 3rd line fires up a test notification via AppleScript – to show you that if everything is working fine … for now. You may omit that third line if you wish.)
Now save the resulting file to your desktop (or wherever else you might prefer), and call it e.g. "fixnotifications.command". – Obviously, you may choose whatever name you desire, but you have to use ".command" as the file extension.
This is how it should look like:

Still, we need to make the file executable, so you can double click it to run it. I recommend the following procedure:
- Open Terminal (via Spotlight)
- Type "chmod +x " (mind the blank space after the "+x")
- Drag the file from the Desktop into the terminal window.
- Now the terminal should look similar to "chmod +x /Users/YourUsername/Desktop/fixnotifications.command"
- Hit enter.
- You may now close the terminal window by clicking the red marble.
Now the file on your desktop should be executable, i.e. double-clickable. Try – and you should see a test notification, saying "Fixed Notifications", plus another terminal window that you may click shut right away.

… Hope that helps.