What is the most secure way to let Alice "input" her private key, transfer it to the server and decrypt the message? What is the most secure way to let Alice "input" her private key, transfer it to the server and decrypt the message? (Then destroy the private key on the server)

Every connection is using SSL.

Exmeple:

Alice log on the website. She have a new "email" from Bob. (Everything is stored in a database, it's not an actual email)

To read it, she needs her private key. How can she do that ? Upload it? Copy the key in a textbox and click submit? (May not be pratical for Alice) Store it on the server (Hugh security issue) ?

(And is it possible to suggest me some keywords please? I'm not used to Crypto.Stackexchange Thank you)
What you really want to do is never have any unencrypted data leave the server in the first place. What should be happening is that the server is sending the encrypted message to Alice, who then decrypts it locally.