In this article, let us review how to generate private key file (server.key), certificate signing request file (server.csr) and webserver certificate file (server.crt) that can be used on Apache server with mod_ssl.
Source: How To Generate SSL Key, CSR and Self Signed Certificate For Apache
The above linked article is an excellent overview that is right to the point for generating SSL keys on a linux server. The instructions include generating a CSR (certificate signing request) that can be sent to a third-party cert authority to get yourself a full-fledged certificate file in addition to instructions on generating a self-signed certificate (often used for testing but handy for a myriad of other things…)
I would also recommend you take a look at this link if you need to generate a key without a passphrase: http://serverfault.com/questions/366372/is-it-possible-to-generate-rsa-key-without-pass-phrase
Enjoy!