By car you can easily reach Öregrund in about 2 hours from Stockholm. From Stockholm you take the E4 towards Uppsala. Then get off on road 288 towards Östhammar, then turn off on road 76.
Bus / Train: Train: From Stockholm, the SL pendulum goes smoothly to Uppsala central. Bus: From Uppsala, bus 811 departs with the final destination Öregrund. This trip takes about 1.2 hours. There are also buses from Gävle (UL 832) and Norrtälje (via Rimbo)