You will first need to get data into the Silverlight app via a web service.
Once this is done, you can export to excel using various methods - search on the internet and you shall find some approaches.
As an example, have a look at this -
Silverlight 4: Interoperability with Excel using the COM Object[
^]. However, using COM is not absolutely necessary - there are other ways too.
Infragistics has an export to excel control.
Or You ycould just loop through data returned by the service and export to excel on your own.