If you can read some Python, the gist of it is in this module:
In the docstring of each of the functions, there’s also a link to the relevant specification document.
If you are interested, I could explain more.
If it’s more from a user perspective: I use this module in PySeedRecvoer:
It’s meant to find the correct seed phrase if you are missing a word or made a typo or something like that. But if you call it with a complete and correct seed phrase and no options to search for something else, it will also just derive the stake key for you:
$ seedrecover ladder long kangaroo inherit unknown prize else second enter addict mystery valve riot attitude area blind fabric symbol skill sunset goose shock gasp grape 2> /dev/null
stake1u9t04dtwptk5776eluj6ruyd782k66npnf55tdrp6dvwnzs24r8yq: ladder long kangaroo inherit unknown prize else second enter addict mystery valve riot attitude area blind fabric symbol skill sunset goose shock gasp grape