Nólsoy is reached by ferry from Tórshavn's main harbour. The crossing takes about 20 minutes and the ferry runs several times a day — check the Strandfaraskip Landsins website for the current schedule, which varies by season. The last ferry back to Tórshavn is typically in the evening, which means day visitors have only a limited window on the island. If you want to see the storm petrel colony (which you do), you need to stay overnight.
The ferry is the only way to reach Nólsoy; there is no bridge or road connection to the main island. Tickets are inexpensive and can be bought at the terminal or sometimes on board. Bikes are allowed on the ferry if you want to explore beyond the village, though the terrain is better suited to walking.