Chuck,
- on the left side of the map click on "More Details..."
- below the little preview picture of the map click on "Open" -> "Open in ArcGIS 10 for Desktop"
- In your MXD that has been open you can just right-click the layer you would like and click "Data" -> "Export Data" (If it is a feature service, just save a local copy for editing)
Hope this helps!