The problem you have is that asmx and WCF are both code-first web service technologies. What this means is that you generally start with classes and the web service stack takes care of exposing your types as XML across the wire.
You are starting with a schema, which is not code. So if you want to use asmx/wcf you need to model your schema in code. You can do this by inferring a class structure from your schema using xsd.exe (or svcutil.exe for WCF).
Alternatively you can model your classes by hand based on the schema definition.
Once you have your classes then you can add declarative attributes to the code (See http://msdn.microsoft.com/en-us/library/83y7df3e.aspx for asmx, DataContract and DataMember for WCF). These attributes control:
- how an incoming stream of XML is deserialized to a type when a service request is received, and
- how instances of your response types get serialized to XML when passed out of your service
The problem with this approach is that getting your XML to validate against your XSD schemas will be a little bit hit and miss, as you cannot rely 100% on class inference from XSD, and additionally you may miss some fine detail if you are modelling it by hand.
Whichever way you do it you need to make sure that your request and response class instances cleanly serialize into XML which will validate against the XSD schemas you have been given.
Also look at a framework called WSCF-Blue which allows you to do contract-first web service design: http://wscfblue.codeplex.com/
Good luck, if you need any more detail about this please let me know via a comment.