What is this effect called and how do you do it?

The intro guitar tone sounds like a completely different tone than the main rhythm guitar; although it may just have a different overdrive pedal. Try one of the fuzz pedals in POD Farm and turn the gain all the way up, it should get you a similar sound.

As far as the drums, it seems like there's just a big room reverb on them with the mix set fairly high!

There might be a high pass filter on the mix/master, but I'm listening on an iPad at the moment so I'm not 100% sure!