First of all, you should turn off the water supply without making any delay as it will stop the dripping of water from the tap. Also advise your family members not to use this tap.
You should use a wrench for removing the head of the tap. Loose it and then remove it from the shaft which is not difficult at all. Many people do this task without even using the crescent wrench.
Now, you should check the gasket, where the tap head was attached with the shaft. Closely observe that there is any leakage or not. You can do this by removing the gasket as well which is basically a flattened doughnut made of rubber.
Then closely check the area where the gasket was attached and also examine the area where the tap head was fixed. If you find any leakage in these areas then mark the area and try to stop the leakage.
Do not forget to clean the tap head and gasket as these areas also cause trouble in the flow of water and sometimes stop water which causes leakage.
If you find that the old gasket has become expired is not in good shape at the moment, then immediately go to hardware store and buy a new gasket. Do not forget to take the old gasket with you which will help in matching the size for purchasing a new one.
Now place the gasket on its place and make sure it sits flat against the head. Also place the head of the tap on its place and screw with your hands. Use crescent wrench to make it tight.
It is time to turn the water supply on. Most probably you will not see the tap dripping any more. However, if it still drips, then call for professional help.