What are the logical steps taken to perform ssh key authentication?

I understand the logical steps of asymmetric key cryptography as it relates to TLS, however, I’ve started using Git and in a bid to avoid having to use a password for authentication, I’ve set up ssh keys for passwordless authentication. I understand that these ssh keys are complements of each other but I do not understand how the actual authentication is taking place. I’ve copied the public key to Git and stored the private key locally. As such, I am able to do what I set out to do (passwordless authentication) but I do not know the underlying steps as to why the authentication is successful. I’ve tried searching the web but every answer I’ve found thus far has been too high level in that they did not specify the steps. For example, were I looking for the TLS steps, I’d expect something along the lines of: Check cert of https page (server) – Grab public key and encrypt secret with it – Securely send secret to server which should be the only entity with the corresponding private key to decrypt – Server and client now switch over to encrypted communications using the, now, shared secret.