I need to retrieve the metadata information from a feature layer. I have the web services available and I can run queries to retrieve the feature attributes, but I don't know any method to retrieve the metadata. Is there any sample or code snippet that I can use to understand the method?
Arcgis Server directly cannot serve the metadata for your geographic data.
I believe that ESRI's Geoportal can do so: http://www.esri.com/software/arcgis/geoportal
I believe that as of ArcGIS Server 10.1 access to metadata for map services is now supported through the REST services:
...The metadata is also available to web developers using a REST request. Developers can append /info/metadata to the end of a service's REST URL to get an XML file containing all the service's metadata. Developers can parse this metadata and present it to the end user of the service in the desired format....
Source and more info here: http://resources.arcgis.com/en/help/main/10.1/index.html#//015400000579000000
Note that I'm not sure if this applies to metadata for individual layers within a map service, or just the entire service as a whole....