Know Before You Go
It takes a small hike to arrive at the hidden oasis: Enter through the gate to Picnic Point at 2000 University Bay Drive, but take the first left after the grassy area. Keep walking on the path and you will find it in its abandoned, slightly graffiti covered glory.
For more info on how to get there, there is a map on the official website for the Lakeshore preserve.
The beach is part of the Lakeshore Nature Preserve that makes up much of the best lakeshore in Madison. The entire lakeshore is maintained by the University of Wisconsin-Madison, so there are well-marked, easy trails to reach every point. It's a great location for a swim or to set up a picnic and relax.