TLS based Server/Client PKI application [on hold]

I want to develop TLS based server/client PKI application. I have successfully created a Self-Signed Server Certificate in Ubuntu using OpenSSL, now I don't know how to install a client certificate in client end and how to establish the communication between the server and client. Please help.

EDIT 1:

I have obtained a personal certificate for the client, and its private key, from a CA. Now how can I install the personal certificate with its private key on the client PC to establish communication between the server and client?