There’s 2 simple steps to set up a tiling background.
First, the image must be able to be tiled graphically meaning if set side-by-side, it must be able to repeat. If you are confused, search for some tillable backgrounds and look at how they’re set up and you can see how the bottom edges are gonna line up with the top portion of tile below it. For example on the site you mentioned, here’s a link to the their image. Hopefully you can see the concept I’m trying to convey.
Second the file needs to be included with your WordPress theme usually in the image folder. In you CSS file you will need to modify the code for the body section to be
#body {
background-image: url(images/HOWEVER-YOU-NAME-IT.png);
}
You can also use the background-repeat: repeat-x;
code to start changing the way the image tiles either on the x or y axis.