A BIP39 seed phrase is first passed through PBKDF2 using 2048 rounds of HMAC-SHA512, alongside the word "mnemonic" concatenated with any additional passphrase as a salt. This produces a 512 bit number.

This seed number is hashed again using HMAC-512. The resulting 512 bit number is split in to a master private key (left 256 bits) and a master chain code (right 256 bits).

The master private key is used to generate a master public key via elliptic curve multiplication.

The parent private key (for hardened paths) or parent public key (for unhardened paths) is then combined with the parent chain code and an index, again hashed using HMAC-SHA512, and further combined with the parent private key to generate a child private key.

This continues down the derivation path as described on BIP44.