Have a look at EnableSession as part of the WebMethod attribute
public class Service1 : System.Web.Services.WebService
{
[System.Web.Services.WebMethod(EnableSession=true)]
public double ConvertTemperature(double dFahrenheit)
{
Session["Conversions"] = (int) Session["Conversions"] + 1;
double temperature = ((dFahrenheit - 32) * 5) / 9;
Session.Abandon();
return temperature;
}
}