It all works the same. WordPress still outputs HTML/CSS, so you can apply the same methods as you would with flat a flat HTML site.
You just need to identify where you’ve used fixed widths in your CSS and create appropriate media queries.
Your ‘header_container’ element currently has a fixed width of 1370px. So when you view the site on a device with a screen narrower than 1370px, you need to create a media query rule so that the element is resized …
E.g. If you were view it on an iPhone 5s in portrait mode (640px wide), you might use …
@media screen and (max-width: 640px) {
.header_container { width: 500px; }
}
Alternatively, you could look at using fluid widths (%) to handle most of the size changes and just use media queries when you want the content to stack properly for mobiles.