To remove the display itself you'll need to apply heat. I had a heat gun - this makes it a lot easier ($20-$30 on eBay) but you could use a hair drier if you don't have a heat gun. For the sake of comparison - the heat gun took around 30 seconds to heat the display completely, which would take 3-5 minutes with a hair drier.

Once the adhesive behind the screen has been heated up, work your way around the edges of the screen with an opening pick or thin rigid guitar pick. The display will begin to separate from the housing.

Once mostly free, carefully lift the display cable through the hole in the top of the phone body. Again; you're replacing this cable completely, so don't worry too much about it.