You _always_ put the public key on the remote server you want to login to. The private key is meant to remain private to you.
So, with ssh, you put the public key into the `authorized_keys` file on the server you want to login to (or have the admin do it, if you don't have the ability yourself).
Now you can use the private key to access that remote server.
In general, you shouldn't give your private key to anyone; that's why it's called private.