If you want to just move the table to a new filegroup, you need to recreate the clustered index on the table (after all: the clustered index is the table data) on the new filegroup you want.
You can do this with e.g.:
CREATE CLUSTERED INDEX CIX_YourTable
ON dbo.YourTable(YourClusteringKeyFields)
WITH DROP_EXISTING
ON [filegroup_name]
or if your clustered index is unique:
CREATE UNIQUE CLUSTERED INDEX CIX_YourTable
ON dbo.YourTable(YourClusteringKeyFields)
WITH DROP_EXISTING
ON [filegroup_name]
This creates a new clustered index and drop the existing one, and it creates the new clustered index in the file group you specified – et voila, your table data has been moved to the new filegroup.
See the MSDN docs on CREATE INDEX for details on all available options you might want to specify.
This of course doesn’t yet deal with partioning, but that’s a whole other story all to itself…