Pugs need very little grooming thanks to their short, smooth coat. Apart from a regular brush with a firm bristle brush, the occasional shampoo is all the grooming your Pug is likely to need. When you do give him a shampoo, do remember to dry him off as quickly as possible to prevent him catching a chill.
Most importantly with a Pug, its skin folds should be cleaned regularly. Because air cannot circulate within the folds it is a breeding ground for harmful bacteria. Make sure you clean your Pug’s facial skin folds at least once a week (more often is preferable). Ear swabs (cotton buds) or tissue are perfectly adequate for this simple task.
For further help and useful information on the grooming needs of your Pug, we can highly recommend: The Pug Handbook by Brenda Belamonte.