What should I do if my computer shuts down unexpectedly?

Reboot............ See what happens.  If it comes up good, fine. If it throws an error it could be software (windows)  a bad driver or a fault in the actual hardware  Power supply, Motherboard or ram.  Remove all peripherals (printer, ext hard drive) everything but the mouse and the keyboard, to exclude them from the problem.  Get it up and running and BACK UP ALL YOUR STUFF to a USB Key or an external hard disk before it fails completely and you lose all your stuff. Try blowing out the computer with canned air to remove all the dust bunnies and crap on your heat sinks.    Good luck.

take it to a repairman -- most common cause is overheating and that's caused by failure of the cpu fan

Panic.  That's what I do.  One time I was freaking out, that I was ready to buy a PC from walmart.  Turned out I needed a new PSU but I needed to be on the computer ASAP.  So I had to wait a day, put the new PSU in and PC was all back up and running.

Update your drivers.
Turn off the Sleep mode.
Turn off Fast Startup.
Tweak advanced power settings.
Use Windows Shutdown Assistant.
Check CPU temperature.
Update BIOS.
Check HDD state.

Be prepared.             

This has happened to me! It was a thermal issue.

If you are using Windows, download "Speccy", run, and look for CPU temperature.
If you are using Linux, search for "desklets", download and run a "temperature monitor" program.

If the temperature is higher than 60C, then either take to a repair place, or, if you feel confident to do it, turn off the computer and open the case.

Find the CPU, press down on the casing of the fan, if it springs back tighten the cooler to the motherboard.
Now turn the computer on with the case open, is the fan spinning? If not replace the cooler.

Press the on/off button to see if it starts up again.

It MAY run through a System Repair if you're running Windows to see if it can 'repair' what the fault that caused the sudden shutdown to occur.

It MAY provide you with an error code, such as STOP CODE such as:CRITICAL_PROCESS_DIED; SYSTEM_THREAD_EXCEPTION_NOT_HANDLED; IRQL_NOT_LESS_OR_EQUAL; VIDEO_TDR_TIMEOUT_DETECTED; PAGE_FAULT_IN_NONPAGED_AREA; SYSTEM_SERVICE_EXCEPTION; DPC_WATCHDOG_VIOLATION, or a series of letters and numbers.  This would provide you with a way to track down what the actual fault was.  (You'll need to type whatever error code is given into the address bar of your web browser, then press Enter to find out what the cause was, and how to go about sorting it out.)