Sometimes, after reboot, you may get a black screen, even before you reach the login prompt! In this case, a likely culprit is the nvidia driver that has not been updated to match any Linux kernel updates that have been applied.
To fix these, the first step is to actually get a login prompt. To do that, reboot the system and at OS-selection screen, select Ubuntu and press `e' to edit its boot options.
Then, find the line that says "ro quiet splash" and change it to "ro queit splash nomodeset". You may also change it to "ro nomodeset" if you wish to get a more verbose boot screen.
After editing the options as such, press "ctrl+x" or "F10". This should start the booting process and hopefully present you with a login screen.
Now, open a terminal and follow the instructions to deal with the nvidia driver by installing it afresh.