If you can no longer access your machine over SSH using your account password than you likely set the following configuration to 'no' in your /etc/ssh/sshd_config file:
# Change to no to disable tunnelled clear text passwords
Once you do this than SSH will only authenticate using a public/private keypair. To enable authentication by username/password again just change this setting back to "yes" (as seen above) and either restart the SSH daemon or restart your pi.
In case you were trying to disable password authentication and move to public key authentication here are the basic steps to make it work:
1). Generate a public/private keypair using openssh (the exact utility is ssh-keygen). This will result in the creation of two files; the public key will end with .pub and the private key should not have any extension. If you accept the default names for these files than "id_rsa" is your private key and "id_rsa.pub" is your public key.
2). Next you need to access your raspberry pi and open the /home/<user>/.ssh/authorized_keys file in a text editor (if no such file exists than create one). Take the entire content of your public key and paste it into this file so that the key is all on a single line. Note that you want everything from the 'ssh-xxx' prefix on the line all the way to the comment at the end (typically something like an email) if you provided one.
3). Next you need to chmod the authorized_keys file so that it is only readable to your user. OpenSSH will generally not trust files that can be opened and modified by any other users on the system.
4). Now you can establish a connection from any machine where your private key exists to the raspberry pi. To do this from command line just provide the -i option and supply the path to your private key. Example: ssh -i /home/fooguy/.ssh/id_rsa firstname.lastname@example.org
The salient point regarding the keys is this:
1). The private key must be on the machine you will be initiating the SSH connection FROM.
2). The public key must be on the machine you are connecting TO (specifically in the .ssh/authorized_keys file of the user you are attempting to connect as).