You need to be sure which part is broken , The Screen it self ? or the glass layer on top of the screen ?
I reed some where that the screen & the protection glass are two separate pieces (each one is sold separately) & the protection glass is allot cheaper than the screen
Assuming that you don't have a film protector over the glass protector, you should be able to feel the edges with a fingernail if the protector AT LEAST is broken. It you can't feel any edges , I'd say the screen is broken but the protector isn't. If you can feel some edges but not all that you can see, then I suppose both the screen and protector are broken.
They have a great video on youtube showing you how to break down the phone and replace it. It wasn't that difficult except feeding the ribbon cable back into the small slot. I think I crimped the ribbon cable and now there is a small part at the top of the screen that doesn't register finger presses. It isn't that big of a deal for me though because you can rotate the screen to select stuff that won't select in portrait.
They send a nice little pry tool with the replacement glass that helps in tearing down the phone. You will also need a T5 torx screwdriver. I had difficulty finding one this small (Radio Shack didn't even have one) So see if you can find one or order one from them with the screen.
I did the same thing to mine. It is fairly simple to change out. Just use a hairdryer to loosen the adhesive and use the pry tool they give you with the glass replacement. Takes 5-10 mins even for a beginner. Be gentle!