This is exactly what I was looking for, but nowhere could I find the steps so simply summed up in a few lines as in your answer. Thanks.
You can find all this information in Chapter 5 "Wallets" of Mastering Bitcoin, although it obviously goes in to the details I have glossed over so can be a bit more technical. I'm happy to try to simply explain any bits you get stuck with. It is available here:
https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch05.asciidocIn terms of BIPs (these will get much more technical and may be over your head), then you'll want to read the following sections:
BIP39: From mnemonic to seed. This explains the first step I described above, of turning a seed phrase in to a 512 bit seed number.
BIP32: Master key generation. This explains the second step I described above, of turning a 512 bit seed number in to a master private key and master chain code.
BIP32: Child key derivation (CKD) functions. This explains turning master keys in to child keys.
BIP44: Path levels. This explains the derivation tree we work down to generate the final child keys which your wallet then turns in to addresses.