typically your pc starts to hang at odd times. if you do a large file move, you'll see it stop halfway through and do nothing for a while then start and stop again. Often windows will tell you due to data corruption you need to run chkdsk, and if the hard drive is actually reporting a SMART error windows will inform you that the hard drive is failing (in windows 8 and 10 it will).
understand that many of these issues can be signs of OTHER problems as well, such as virus infestation, driver problems or overheating. so you probably won't know for sure unless you run a hard drive diagnostic.
Windows event viewer in the system event log may start reporting failures on the drive as well (typically hard drive 0)