Linux – How to ssh without a password (setting up ssh keys doesn’t work)

I want to ssh, scp, git fetch, etc. without a password. I saw the previous questions, and closed ones regarding this issue, but the suggestion seems to be to use ssh keys. However, after setting up ssh keys, I am still asked for my password (it's not asking for my private key password; it's asking for my login password). How am I supposed to set this up so that it only uses my private key for authentication?