Golf is a non-contact, somewhat refined sporting activity. It's usually a pastime of the rich and successful, so a golf logo would have to cater to this demographic in the world. Organizations that require such a golf logo would probably be golf resorts, golf clubs, or golf courses.
Like the game itself, golf logos need to convey their message in a simple and clean manner. This is why its design styling should be on clean lines, bright but not scorching colors, and a bit on the minimalistic side. Unless the golf logo is for a minigolf that wants to attract children as their audience, there shouldn't be any garish colors or cartoon used.
First of all, you should evaluate your company and see what its offering. This would help in creating a logo that conveys the right message for your audience.
Creating the logo design might be a bit tricky, since you also have to keep it simple while being representative of what you're offering. You can be creative here too, with the simple profile of a golfer taking a swing with a club. The white space surrounding the golfer might convey another picture; that of a warrior helmet, for instance. This would be great for a company that holds golfing competitions on the regular.
Since golf conjures up the image of rolling green fields, the skies, and trees, try to incorporate natural colors like green and blue in your logo. The font utilized should be as minimalistic as the logo itself for most cases, since this gives a feeling of luxury. You may want to consider the fonts AvantGarde BD BT or Engravers Gothic BT for this purpose.
If you're struggling to design a golf logo on your own, head to the experts. Hiring a professional logo graphic designer would ensure that you're on the right track towards attracting your audience.