Considering the following tables (table_1 with IDENTITY column):

IF (object_id('table_1') IS NOT Null)
drop table table_1

CREATE TABLE table_1
   (
     Id bigint IDENTITY(1,1) NOT NULL, 
     Col1 nvarchar(4000) NOT NULL,
     Col2 nvarchar(4000) NOT NULL
   )

Id (identity)    Col1    Col2

-----------    ----    ----

IF (object_id('table_2') IS NOT Null)
drop table table_2

CREATE TABLE table_2
   (
     Col1 nvarchar(4000) NOT NULL,
     Col2 nvarchar(4000) NOT NULL
   )

Col1    Col2

----    ----

Insert some data into table_2:

INSERT INTO table_2 VALUES ('some text', 'some other text')
INSERT INTO table_2 VALUES ('some text', 'some other text')
INSERT INTO table_2 VALUES ('some text', 'some other text')

...

The following syntax must be used when trying to populate table_1 with records from table_2 using INSERT INTO SELECT statement:

INSERT INTO table_1 (Col1, Col2) 
   SELECT Col1, Col2 FROM table_2

The result will look something like this:

select * from table_1