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.
You can recreate it by adding a noise filter to a colored layer.
Then use transparency to make it more subtle. You can also invert the layer colors if you want a light noise effect instead.
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:
Noise Filters in GIMP
Below are examples of factory noise filters in a default GIMP 2.6 installation.
Source image (unfiltered)
By choosing different settings or combining these effects we can achieve anything from subtle to impressive effects:
HSV noise (2) with stronger effect setting.
Additional noise filters can be added from the GIMP Plugin Registry. The Film grain script (1) is not installed in GIMP 2.8. but can also be added from the plugin registry.