How can I access data stored in a separate table from my WebServices?
What do you mean by "WebServices"? ArcGIS Services?
If you have the table as one of the layer within a MapService, you can access it like a regular Layer, except if will not contain any geometry information and cannot use FeatureLayer. But you can use, QueryTask like any other layer.
WebServices should be MapService, my mistake. Also the tables in question were joined and a join class reference was made from within the ArcGis Desktop before I published the MapService.
Retrieving data ...