Berkeley Park is on the south bank of the Missouri River between the ASB and Paseo bridges. Easiest way to get there (though perhaps noe least convoluted): Take I-35 North from as close you can jump onto it until you get to the Front Street exit, just before you cross the Paseo Bridge. I believe at that point you'll turn left, swing under the bridge, and then your first right takes you directly into the park.

Though I doubt you'd come the other way, but if you're in downtown KC, head north on Grand. As Grand crosses 3rd Street, it goes up a bridge that curves to the right. This road leads directly into the other end of the park.

I know that part of town like the back of my hand. It is holy ground to me.