Key authentication is more secure over password authentication. Just because users might have weak passwords, an attacker can easily brute force them. On the other hand, it's impossible to brute force ssh key. That's why I encourage you to use ssh key authentication and below I will show you how to configure it.

Client part

1. Generate key on client machine.

ssh-keygen

You will be asked to enter path to your key, default path would be OK. Also you may enter passphrase or leave it empty.

2. Copy public key to ssh server and remove it from client machine.

scp yourkey.pub username@yourserver.com:~/
rm yourkey.pub

Server part

3. ssh to your server using password.

ssh username@yourserver.com

4. Create .ssh directory, set permissions

mkdir -p ~/.ssh
chmod 700 ~/.ssh

5. Append public key to authorized keys, set permissions:

cat ~/yourkey.pub >> ~/.ssh/authorized_keys
chmod 600 ~/.ssh/authorized_keys

6. Edit /etc/ssh/sshd_config using any text editor and set the following settings:

RSAAuthentication yes
PubkeyAuthentication yes
PermitEmptyPasswords no
PasswordAuthentication no
ChallengeResponseAuthentication no
UsePAM no

7. Reload configuration for your ssh service (or restart):

sudo service ssh reload

8. Now ssh to your server using password and make sure you get permission denied error.

ssh username@yourserver.com

9. Finally, ssh to your server using private key. You should successfully connect without any password prompt.

ssh -i yourkey username@yourserver.com