To verify if you have protected, run this command and check for built on to be greater or equal to April 7th, 2014:
$ openssl version -a
OpenSSL 1.0.1e 11 Feb 2013
built on: Mon Apr 7 20:33:19 UTC 2014
platform: debian-amd64
The way SSL/TLS works is that the client and the server must agree on a cipher to use for encryption. If you were to attack a server, you would obviously use the least secure cipher. To protect against this, simply disable ciphers to be known as weak or those which flaws have been discovered.
I am using this configuration for Apache:
SSLCipherSuite ALL:!ADH:!AECDH:RC4+RSA:+HIGH:+MEDIUM:!LOW:!SSLv2:!EXPORT
For Nginx, see their configuration reference. Since 1.0.5, they are using a sensible default. Otherwise, you can use the same as above.
The private key must never be discovered. Otherwise, anyone could decrypt the content and could perpetrate a MITM attack. If the private key is too weak, it could eventually be guessed given enough data. However, SSL/TLS handshakes are very CPU intensive for both the server and the client. Using a key too long will considerably slow down your website. In most cases, 2048 is perfect.
SSL Labs provides a free test suite that will test your ciphers and for known attacks including BEAST and Heartbleed. This is a must: https://www.ssllabs.com/ssltest/
I am not a security expert, I simply happen to have done hosting for quite a time. I suggest you do not take my word blindly and go check this very pertinent paper from SSL Labs.