First let's try to figure out if the screen really is dead. Take the battery out and put it back in. Now, press and hold the Power, Home, and Volume Down buttons for about 10 seconds. This should take you into recovery mode, and this is the most basic state of your phone. If your screen doesn't display anything here, then things get a little more complicated.
Your screen might not turn on because the fall made an internal connector get loose, in which case you could just try to open up the phone, locate the connector, and place it back where it belongs, or it can be that the fall did break something inside.
My recommendation, if you've never attempted to repair a phone before, is don't chance it. Take it in for repairs unless you're willing to buy the whole screen+digitizer and follow some video on how to replace it on your own.