As the other answers suggested, you can use the INSERT ... SELECT
syntax to do something like this:
INSERT INTO brands (brandName)
SELECT artBrand
FROM original
GROUP BY artBrand;
INSERT INTO articles (artName, brandID)
SELECT o.artName, b.brandID
FROM original o
JOIN brands b ON (b.brandName = o.artBrand);
Test case:
CREATE TABLE original (artID int, artName varchar(10), artBrand varchar(10));
CREATE TABLE articles (artID int auto_increment primary key, artName varchar(10), brandID int);
CREATE TABLE brands (brandID int auto_increment primary key, brandName varchar(10));
INSERT INTO original VALUES (1, 'TNT1', 'ACME1');
INSERT INTO original VALUES (2, 'TNT2', 'ACME1');
INSERT INTO original VALUES (3, 'TNT3', 'ACME1');
INSERT INTO original VALUES (4, 'TNT4', 'ACME2');
INSERT INTO original VALUES (5, 'TNT5', 'ACME2');
INSERT INTO original VALUES (6, 'TNT6', 'ACME3');
INSERT INTO original VALUES (7, 'TNT7', 'ACME3');
INSERT INTO original VALUES (8, 'TNT8', 'ACME3');
INSERT INTO original VALUES (9, 'TNT9', 'ACME4');
Result:
SELECT * FROM brands;
+---------+-----------+
| brandID | brandName |
+---------+-----------+
| 1 | ACME1 |
| 2 | ACME2 |
| 3 | ACME3 |
| 4 | ACME4 |
+---------+-----------+
4 rows in set (0.00 sec)
ELECT * FROM articles;
+-------+---------+---------+
| artID | artName | brandID |
+-------+---------+---------+
| 1 | TNT1 | 1 |
| 2 | TNT2 | 1 |
| 3 | TNT3 | 1 |
| 4 | TNT4 | 2 |
| 5 | TNT5 | 2 |
| 6 | TNT6 | 3 |
| 7 | TNT7 | 3 |
| 8 | TNT8 | 3 |
| 9 | TNT9 | 4 |
+-------+---------+---------+
9 rows in set (0.00 sec)