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:
Below are examples of factory noise filters in a default GIMP 2.6 installation.
Source image (unfiltered)
Various highly configurable noise filters with default settings
(1. Film grain 2. HSV noise 3. Pick 4. RGB noise 5. Slur 6. Spread)
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.