I originally tried to set up a generic set of directions, but they didn't work too well.
Use this link to Yahoo's map generator.
The Capitol building is at 1445 K Street, Lincoln, NE 68508. For Antelope park, use 2740 A Street, Lincoln, NE 68502
Using these street addresses, you can generate directions and even maps from your front door.
Once you find Antelope Park, enter. The road forks, you can take either direction. To the left you will come to a parking area. Park your car. The bandshell will be to the south west of where you parked. You can also go straight, and curve around the bandshell. Just keep curving left and you too will come to a parking area, albiet a larger one. This one is also closer to the shell, so I would recommend you use it. Can't miss the festivities from that spot!
If these methods don't work, you can mail me at redgrailne@aol.com and I'll send you personal directions. If you are in a pinch, you can call 402-476-7178.
Blessed Be! Jason.