OK. I've set up two tables (I'm testing this locally on my Mac using MAMP and phpMyAdmin). First problem was that I couldn't work out how to assign recordingArtistID as a foreign key in the recordings table to artist.artistID - I've already got a primary key set in both tables and it just kept throwing errors whenever I tried, so at the moment the foreign key is recordingID - couldn't see how to make recordingArtistID the foreign key.
The first page works fine, but the problem comes in the recordingsResults.php page - I think I might have messed up here as it's showing all the results from the database rather than pulling them for a specific artist. Have I misunderstood what you mean by passing the recordingID column as a querystring variable?