If the schemas of the two tables really match:
INSERT INTO newTable
SELECT * FROM oldTable
If not, you will need to supply the column names (the column list for newTable is optional if you are selecting columns in the same order as newTable's schema and specifying values for all columns):
INSERT INTO newTable (col1, col2, col3)
SELECT column1, column2, column3
FROM oldTable
I hope this helps you.