How to make a table with fields that are other tables in MySQL?
This is a really basic example of normalization.

Typically you set up a foreign key relationship.  In your example you would have two tables:

Artists - id, name, etc...

Songs - id, artist_id, name, etc...

You would retrieve needed data from Artists using a JOIN.  You should look into some entry level SQL tutorials.  JOINs are the bread and butter of SQL, and what makes it a relational database.