How would I go about making a texture similar to the one used throughout this site:
Is it some kind of noise pattern?
Yes, it’s a noise effect that you can recreate using Photoshop or CSS. You can see it better in the background image of the website.
Noise Effect in Photoshop
You can recreate it by adding a noise filter to a colored layer.
Filter > Noise > Add Noise..., and select the Amount.
Then use transparency to make it more subtle. You can also invert the layer colors if you want a light noise effect instead.
Noise Effect in CSS
There is also a CSS script that created noise. I haven’t tried it but it looks really good, I didn’t know it existed. It’s called CSS Noise, and all you need to do is call it using a class: