The only way to reach La Graciosa is by ferry from Órzola on the northern tip of Lanzarote. The crossing takes about 30 minutes. Líneas Romero operates several departures daily, more in summer. Day trippers fill the morning boats; if you are staying overnight, the afternoon ferries are calmer and cheaper.
There are no cars on La Graciosa — officially it is the largest car-free inhabited island in Spain. Bicycles and walking are the only options once you arrive. You can bring a bicycle on the ferry.