If the web service is basic asmx web serivce,then you can use WSDL.exe tool to create client proxy class for the XML Web service and add this generated client proxy class to your project,finally you can use the web method of web service.
1,Web Services Description Language Tool (Wsdl.exe)
As suresh_g_v2002 mentioned, you can also call Web Service or WCF REST Service asynchronously using ScriptManager.
2,Consuming a WCF / ASMX / REST Service using jQuery
Consuming a WCF / ASMX / REST Service using jQuery
If the web service is ordinary WCF service,you can directly add service reference within the project explorer or use svcutil.exe to generate client proxy class.
In .Net without adding reference to the project we can call in the following ways
1. Using HttpWebRequest of System.Net namspace..,
2. We can also call webservice asynchronously using Scriptmanager.
[ Bit of googling can solve the problem