How to move a table to secondary filegroup without losing data?
How to move a table to another filegroup?


You need to rebuild your clustered index to new filegroup


  How to move a Heap table to another filegroup?


You need to organize it as a clustered index to new filegroup


  Do we need to move the Non-Clustered indexes to secondary filegroup after moving the table?


Yes, you can move nonclustered indexes to new filegroup.
Ent Edition Of SQL allows you to even rebuild indexes online.
Some links:
https://msdn.microsoft.com/en-us/library/ms175905(v=sql.105).aspx