You need to create a simple trigger with AFTER INSERT, which means the trigger will run after insertion is done.
You will get the inserted values of your table from temporary INSERTED table in your trigger.
Below is the sample code.
CREATE TRIGGER [dbo].[TR_Insert_Simple] ON [dbo].[Simple] AFTER INSERT
INSERT INTO SimpleHistory (column names) SELECT * FROM INSERTED
DELETE FROM [Simple] Where PK_ID = (SELECT PK_ID FROM [INSERTED])
Hope this helps you.