Select data from a table in chunks, perform lookup and insert into another table

One of the simplest ways to move data between tables in chunks is:

DECLARE @CHUNK_SIZE int = 10000;
DECLARE @RC int = @CHUNK_SIZE;

WHILE @RC >0
BEGIN
    INSERT INTO TargetTable (Mycolumns)
    SELECT  TOP @CHUNK_SIZE Mycolumns
    FROM    SourceTable
    WHERE   Conditions
    ;
    SET @RC = @@ROWCOUNT
    ;
END

Where the conditions need to exclude already processed rows.
The performance is mostly depending on these conditions (and indexes).
You can for example use NOT EXISTS, or use an ordered query and set a variable = Max(ID) from the output clause, or you can remove processed rows from the Sourcetable.
But as you've already been told, we don't have enough information to tell you the best way.