When you start Windows 8 in Safe Mode, you start it with only the processes absolutely necessary for Windows to be usable. If Windows 8 does start properly in Safe Mode, you can then troubleshoot to see what driver or service might be causing the problem that's preventing Windows from starting normally.
See How To Access Advanced Startup Options in Windows 8 for instructions on the six different methods to open this very helpful menu of repair and troubleshooting tools.
Once you're on the Advanced Startup Options menu (shown in the screenshot above) then move on to the next step.
The Windows 8 Safe Mode Catch-22
Of the six methods for opening Advanced Startup Options outlined in my linked instructions above, only methods 1, 2, or 3 allow access to Startup Settings, the menu that Safe Mode is found on.
Unfortunately, those three methods only work if you have access to Windows 8 in normal mode (Method 2 & 3) or, at very least, get to the Windows 8 sign on screen (Method 1). The irony here is that few people who need to start in Safe Mode can get all the way to the sign on screen, let alone start Windows 8 normally!
The solution is to open Command Prompt from the Advanced Startup Options menu, which you can do using any of the six methods, including Methods 4, 5 & 6, and then execute some special commands to force Windows 8 so start in Safe Mode on the next reboot.
See How To Force Windows to Restart in Safe Mode for complete instructions. You won't need to follow this tutorial if you start Windows 8 in Safe Mode that way.
Tip: If Windows is working fine for you right now but you still want to start Windows 8 in Safe Mode, another way is to make boot option changes from the System Configuration utility. See How To Start Windows in Safe Mode Using System Configuration, in which case you can skip this tutorial entirely.
What About F8 and SHIFT+F8?
If you're familiar with previous versions of Windows like Windows 7, Windows Vista, or Windows XP, you may remember that you could force the loading of what was then called the Advanced Boot Options menu by pressing F8. This is no longer possible in Windows 8.
In fact, even the widely publicized SHIFT+F8 option, which supposedly works to force Advanced Startup Options to appear (and ultimately Startup Settings and Safe Mode), only works on very slow computers. The amount of time that Windows 8 looks for SHIFT+F8 is so small on most Windows 8 devices and PCs that it borders on impossible to get it to work.
Not Using Windows 8?
See How Do I Start Windows in Safe Mode? for specific instructions for your version of Windows.