Hot, Soapy Water and a Toothbrush
The simplest, and perhaps least dynamic, way to remove unwanted grit and grime from the face of your clubs is a bucket of hot, soapy water and a toothbrush. Fill a bucket with hot water and 1/4 cup of dish soap, place your dirty clubs in the bucket and let them soak for about 1/2 an hour. This will loosen up the dirt. Once they've soaked for the proper amount of time, take them out one by one and rub them down with a toothbrush. A toothbrush is perfect because it isn't abrasive and its small bristles are able to get in the tight grooves in the club face. Put each club back in the bucket to rinse, and then wipe them down with a soft cloth.
Another way to get your golf clubs good and clean is with an abrasive cleaner like Comet or Bar Keepers Friend. Because clubs are made of steel they are pretty resilient to scratching, and a good abrasive cleaner presents a strong formula for removing not only dirt but tee marks and heat marks. Once again, soak your clubs in a bucket. Then take each club out, spread a little abrasive cleaner on a sponge and gently rub the club face. Rinse the clubs in the bucket and wipe dry.
You can purchase club cleaner at the pro shop or online. Club cleaner is really nothing more than a glorified toothbrush, except its bristles tend to be a little more resilient than your standard beat-up toothbrush. It also comes with a metal tool that cleans out the grooves of the club. Once again, the most effective way to use a club cleaner is in conjunction with a bucket of hot, soapy water.