Certificate for the public key I am new to Network Security and learning about various security features like Diffie-Helmann and others. 

I understand that the Public key send by the server to the client needs to certified that it is authentic. So, a Certificate Authority (CA) needs to sign the public key. But I would like to know how is this public key signed in the certificate. Using some private key? And if so, how does the client decrypt this certificate and finally get the public key of the server? For example: how does it work in case of a TLS handshake?
The certificate is not encrypted.  It contains signatures (basically hashes) that are encrypted with the private key.  The public key can decrypt that and the hash can be verified.  In SSL/TLS there is a signature that the client supplies via private key to prove they are the owner, and the CA has signed it the cert with their private key, which can be verified using a CA cert you mark as explicitly trusted.