Assuming you have not yet generated your public keys you will need to do that first.
This will generate and store rsa keys in your ~/.ssh directory particularly the public id goes in ~/.ssh/id_rsa.pub file. To copy this you can cut and paste the contents into the authorized_keys file, making sure the file permissions do not allow the file to be read by users other than the owner. A simpler method is to use the following
ssh-copy-id -i ~/.ssh/id_rsa.pub remote-host
At this point you can login without providing a password.