Hydra has a telephone exchange operated by the National Provider OTE. The dialing code for the island is 22980 and this code even when you're on the island is required with the actual telephone number. The country code for Greece is 30.
There are public phones, that take phone cards only, outside the post office and next door to the Municipality Offices on the west side of the Cathedral. Phone cards are available from many of the general shops on the harbour front and from the island's supermarkets.