Method Overloading in Web Services is a very useful for
SOA applications.

We need some additional configuration for achieving this,

Important:Just set

WebServiceBinding(ConformsTo = WsiProfiles.None)

See this Sample Class with Overloaded Methods.

using System;
using System.Web;
using System.Web.Services.Protocols;

[WebService(NameSpace="http://tempuri.org")]
[WebServiceBinding(ConformsTo = WsiProfiles.None)]
Public class Service:System.Web.Services.WebService
{
  public Service()
   {
   }

[WebMethod (MessageName="Adding Interger Fields")]
public int Addition(int Num1,int Num2)
{
  int Num3 = Num1+Num2;
  return Num3;
}

[WebMethod (MessageName="Adding long  Fields")]
public long  Addition(long Num1,long Num2)
{
  long Num3 = Num1+Num2;
  return Num3;
}

}

Now,i felt you can understood how to apply Method Overloading in Web Methods.

Happy Coding.