I am able to build the artist database and the song database, but I am not able to do the "Add Another Song", all I can do is create 100's of separate fields, or 1 data entry box where they are all listed together.
First thing you need is a another table – a so-called join table that combines a songwriter and a song (in particular, two IDs from either table); this allows you to store many songs for a songwriter (all join table records related to a songwriter, each pointing to a song record) , and specify any number of songwriters for a song (all join table records related to a song, each pointing to a songwriter record).
This is usually shown as
Songwriter --< SongwriterInSong >-- Song
I suggest you first study how to implement the join table (and get familiar with IDs / foreign / primary keys); then come back and ask about your intended workflows.
Eroist you’re a legend, thank you!