Unless you have your own sailing yacht, you'll have to use the public transportation which means the ferries:

Ferry

Four daily ferries link Ios to Piraeus (7 hours), Paros (2, 5 hours) and Naxos (1 hour and 15 minutes).

Daily ferries sail to Santorini (1 hour) and Mykonos (4 hours).

Five weekly ferries go to Sikinos (20 minutes) and Folegandros (1, 5 hours).

Four ferries per week link Ios to Anafi (2 hours) and two weekly to Syros (2 hours and 45 minutes).

One ferry a week goes to Amorgos (2, 5 hours), Kimolos (2, 5 hours), Milos (3, 5 hours), Sifnos (5 hours), Serifos (6 hours) and Crete (6 hours).

Flying Dolphins (hydrofoils)

Three daily Flying Dolphins and more link Ios to Santorini (30 minutes) and Naxos (50 minutes).

Two to three daily hydrofoils go to Paros (1, 5 hours), Mykonos (2 hours and 45 minutes) and Tinos (3, 5 hours).

One to two daily Flying Dolphins go to Syros (2 hours and 15 minutes).

Six weekly Flying Dolphins leave from Ios to Sikinos (10 minutes) and Folegandros (45 minutes), four weekly to Amorgos (2 hours) and three weekly to Anafi (1 hour).

Two weekly hydrofoils sail to Koufonissia (3, 5 hours), Shinoussa (3 hours), Iraklia (3, 5 hours) and Crete (2 hours and 45 minutes).

One weekly Flying Dolphin goes to Donoussa (2, 5 hours).

Catamaran

Daily Catamarans link Ios to Santorini (30 minutes), Naxos (50 minutes), Paros (1, 5 hours), Syros (2 hours and 45 minutes) and Rafina (4 hours).