Username and Password: How does it work?
"Will they just scrap all the previously negotiated keys and switch to TLS-PSK with

Password-Authenticated Key Agreement or Password-Based Key Derivation?"

No.

"What will happen next?"

"Could you please describe how client and server use username and password?"

"What are the steps and algorithms used in this?"

The server will look up the username's salt, hash the password with it, and then compare

the result to the stored password has. ​ If they are equal, then authentication succeeds,

else authentication fails. ​ The algorithms used in this are PBKDF2,bcrypt,scrypt.