During the development of Asp.Net application, developer don't need to instantiate any session. Session is automatically instantiated, you need to use them according to your requirement. Here, I am going to show you one simple example.
DataTable dt = new DataTable();
// what ever the table you want to put in dt
// assign dt value into session variable, make sure it is unique name,
// I have given dtSessionVariable as session variable name.
Session["dtSessionVariable"] = dt;
// To retrieve it from session, it require casting back to original type
DataTable dt = (DataTable)Session["dtSessionVariable"];