In your site you’ll have some tags in the <head> section.
You need to add the appropriate <meta name="twitter:card" ... (and other) tags in that <head> section. You can find examples in the “Sample Code” section for each card type.
Since you’re using Wordpress, this actually isn’t going to be easy, as every post will need a different set of tag content, and Wordpress is a dynamic PHP application. We worked with the guys over at Wordpress to create our own official Wordpress plugin. Maybe you could take a look at that?