X.509 Certificate validation with Java and Bouncycastle

Question

through the bouncycastle wiki page I was able to understand how to create a X.509 root certificate and a certification request, but I do not quite understand how to proceed concept- and programming wise after that.

Lets assume party A does a cert request and gets his client certificate from the CA. How can some party B validate A's certificate? What kind of certificate does A need? A root certificate? A 'normal' client certificate?

And how does the validation work on programming level, if we assume that A has successfully send his certificate in DER or PEM format to B?

Any help is much appreciated.

Best Regards, Rob