I've only worked with private keys when I was the one setting up for both servers. However, this time, I was given private keys to be used as password to login to the server from my local.
Anyone can help/show me how?
ssh -i /path/to/private/key remoteuser@remotehost
Note that the private key will need appropriate permissions (0600)
If you are on Windows, you'll probably want to use Putty, and when you create a new profile you'll be able to select a key. Note that your key may need be be converted to a different format (eg pem -> ppk) , but Putty has directions on that using the puttygen utility.
You can also save the private key as ~/.ssh/id_rsa (0700 directory permissions and 0600 file permissions) and then ssh user@host.
It would be expected that on the other hose, your public key would be in the ~/.ssh/authorized_keys file.