As far as I'm aware your basic subscription to channels should remain the same price, but you will NEED the SkyHD Pack, which gives about 26 channels in HD for an extra �10 per month (check the Sky website for details on these), in order to get HD channels.
Its a good start if they are willing to give you a box and do an install for free!
But remember you will need an HD ready TV set and and HDMI cable to connect the new SkyHD box to the TV to actually get the benefit of HD.
Hope this helps.