How can SSL secure a two-way communication with only one key-pair? As I understand it, SSL involved the use of a public-private key pair.  How does this enable two-way communication?

Suppose I have some server with which I wish to communicate securely.  I connect to it, and it supplies me a certificate, which contains its public key (assume the certificate is valid).  I then take my request, and encrypt it with this public key, and transmit the resultant ciphertext to the server.   This communication is secure from eavesdropping.  But how does the server return to me my results securely?  I lack a public/private key pair, and have no certificates.
That's not quite correct.  In SSL, two things happen:


First, a session key is negotiated using something like the Diffie-Hellman method.  That generates a shared session key but never transmits the key between parties.
Second, that session key is used in a normal symmetric encryption for the duration of the connection.


SSL does use public/private in one way, because an X509 certificate is used to identify at least one end of the connection.  Those certs are signed using an asymmetric key pair.