What steps do you have to take to own the masters of your songs?

It is called a contract.

You have it all spelled out in advance of ever doing any work for the studio or producer.

The original authors of songs, by default, own all rights to music. Musicians own rights to the recorded performance so in both cases authors own the music and musicans share performance rights by default. Those rights are "property rights" and can be bought and sold by contract.

You have to pay whoever made the recordings.

Depends on why you don't own them in the first place. There's presumably paperwork somewhere, like a record contract. You'd start by reading it.