Really just an islet, Quiste is overgrown and vacant, and a scant 100 meters long—a perfect place to pitch a tent and camp. Many Moyogalpa [1] hotels will help you make arrangements with someone with a small boat.
Otherwise, in Charco Verde [2], Rubén Riveras will drop you off on the island in his motorboat and pick you up again later (or the next day) for about $15, depending on the number of travelers.
But you can just as easily strike a deal with any of the locals in the small communities to the north of Moyogalpa, like Barrio de los Pescadores.
Links:
[1] http://www.moon.com/destinations/nicaragua/ometepe-and-rivas/la-isla-de-ometepe/moyogalpa
[2] http://www.moon.com/destinations/nicaragua/ometepe-and-rivas/la-isla-de-ometepe/moyogalpa/sights/reserva-charco-verde