Credit card payments on site

I have a client that want to set up a store online. They want it to be easy, so I was going to use Wordpress (as I'm familiar with it) and a store plugin from http://instinct.co.nz/. The trouble is they don't want to use Paypal or any service like that and want direct credit card payments.

What is the easiest way of doing this (as long as it's properly secure)?

I understand they would need a https secure certificate also, but don't fully understand all of this.

Any help, links, info, advise would be great. Many thanks.