I'd try the Application Scenario's, Guidelines and How Tos sections of this CodePlex Link. You should be able to find a scenario that matches closely to yours and follow the guidelines and configuration to get yourself going.
If I've understood this correctly, the client application would pass a username/password to your silverlight app which would require a wsHttpBinding that has clientCredentials="Username". You would need to be able to authenticate this against a user store configured on your server, for example you could configure a SQL Server provider.
I'm not sure how your 3rd party client app works, but you would require a seperate security configuration for that communication. You could use a less secure binding if the apps were on the same machine and possibly use clientCredentials="Windows"/"None"/"Basic".
Difficult to advise further without knowing your exact situation. What do you have so far?