SQLite has limited ALTER TABLE support that you can use to add a column to the end of a table or to change the name of a table.
If you want to make more complex changes in the structure of a table, you will have to recreate the table. You can save existing data to a temporary table, drop the old table, create the new table, then copy the data back in from the temporary table.
For example, suppose you have a table named "t1" with columns names "a" and "c" and that you want to insert column "b" from this table. The following steps illustrate how this could be done:
BEGIN TRANSACTION;
CREATE TEMPORARY TABLE t1_backup(a,c);
INSERT INTO t1_backup SELECT a,c FROM t1;
DROP TABLE t1;
CREATE TABLE t1(a,b, c);
INSERT INTO t1 SELECT a,c FROM t1_backup;
DROP TABLE t1_backup;
COMMIT;
Now you are ready to insert your new data like so:
UPDATE t1 SET b='blah' WHERE a='key'