Start with Event Logs. See if the PC is being shut down gracefully or if it is perhaps BSODs. Even if the system is just cutting off, they maybe some warning events that trigger before it goes down.
Lacking any of that, begin with testing the power supply. The PSU is the most likely component to fail in a PC. Next look for heat issues. Failure of fans or old dried heat sync compound. Dust build up. Make sure memory and any peripheral cards are properly seated. Consider using a UPS unit in case of dirty power from the main line.
After that test the memory. Stress tests with Prime95.