When I use the word fundamental I hesitate, because I can easily think of a great player that is not doing it. However, I consider the grip to be the most important and fundamental technique that a golfer can learn. No single aspect of golf mechanics will add or reduce power, trajectory, curve, or a sense of touch more than the golfer’s grip.
I believe that all elite golfers are vigilant about maintaining their grips, constantly making small adjustments for desired ball flights and short game shots. As far as grip pressure goes, it should be light. Hold the club, don’t squeeze it. A light grip is crucial to learning timing, a powerful release, the loading and unloading of a club, which has flex for a reason. There aren’t a lot of constants when learning golf, but a light grip is one of them. Never squeeze the club! Whether it is an extra long drive that you desire, or to feel steady over a fast, five foot putt, a light grip is the ticket. Tiger Woods has said that when he really wants to crush a drive, he “holds the club lighter and takes it away slower.” He also said that his biggest breakthrough as a professional was when he spoke to Ben Crenshaw about his putting. Crenshaw suggested he significantly lighten his grip pressure. Crenshaw’s grip was so light that the putter was nearly falling out of his hands.
A proper grip is some form of a Vardon grip. Interlock, overlap and ten finger grips are your choices (although I’ve seen cross-handed work well!). Each of these three grip options have different benefits and acceptable in my book. A good instructor will look at your grip first, in every lesson. If the grip is proper, the club won’t shift around in the golfer's hands during the swing. The hands will tighten on their own during the downswing, like a knot, or a Chinese finger trap. Once the grip is in the correct position, the club-head is allowed to rotate fast and freely. It is not guaranteed that the club will be perfectly square at impact, but it sure increases that likelihood!
Every person's swing is different, based on variations in size, flexibility, athleticism etc. I look at a swing as a manifestation or symptom that is the result of root causes. The grip is the prime source. A swing makes compensations for the grip in good and bad ways. As a teacher, I’m not going to move onto anything in the swing unless the grip is proper and light.