Assume that your host computer is A, the other one that needs to login via SSH is B.
First, generate keys.
Run this command in both A and B:
ssh-keygen
Then exchange public keys.
Create a file named authorized_keys
in ~/.ssh
in B. Open ~/.ssh/id_rsa.pub
in A and copy its content to ~/.ssh/authorized_keys
in B.
Create a file named authorized_keys
in ~/.ssh
in A. Open ~/.ssh/id_rsa.pub
in B and copy its content to ~/.ssh/authorized_keys
in A.
Now you can get rid of password.