When you win the after hours park party you are given a wristband (right then and there... when you win it) that signifies that you are a part of the event. You also usually get a button that says something like "My Dream Came True" which shows everyone that you won a prize (this button is usally only given out for the prizes that you are not physically being handed...you will not get this if you win a hat, fastpass or lanyard). They will have transportation running for the event so that you can get to and from your hotel or other areas on the property, and only those people that have the wristbands will be admitted into the park.
Also when you win they will advise you were to meet and at what time. Usually it is somewhere in the park for a psuedo welcome party if you will, which really is just an area that they clear out early so that they can clear the rest of the park of day guests prior to the event for prize winners. You would (or should) have all the information presented to you at the time the prize is won.
