Not every hairstyle requires a part, but they are common nonetheless. Both men's and women's hairstyles feature parts, and they are common in short, medium and long hairstyles alike. When parting the hair for the first time, it's sometimes difficult to tell where the part is.
Look for a natural part. It's sometimes obvious which side hair parts on. If there is a natural break in the hairline on one side, the part may naturally be there. Cowlicks also force a part on a certain side. If there is a cowlick that forces hair a certain way, part with the cowlick. Trying to fight against a cowlick is a lost battle from the beginning, since it's not possible to change which way the hair naturally grows.
Try each way. If there's no indication of which way the hair goes, try parting it both ways. Go with a part on the left side one day and part it on the right side the next. If one way seems more comfortable, go with it. If there are no comfort issues, just decide which way looks better.
If you end up unhappy with the side you've picked, you can always change it later. It's not a permanent decision.
Ask a hairstylist; he's a professional who deals with hair constantly. By examining the hair, head and scalp, a stylist can tell where the part should go. He can also demonstrate exactly how he determined this, which is extremely helpful for future hairstyling. Watch in a mirror when the stylist parts the hair to make sure it goes the same way later.
At the end of the day, look at your reflection in the mirror. Focus on where the hair naturally falls to the side. The end of the day works best because there's no hair product left in the hair, and it's dry and natural. Flip your head over and let the hair fall, and see if a part is visible.