From the Old Port in Mykonos, close to the city center and the church, you can take a ferry to Delos. In the morning there is a boat at 09h00, 10h00 and 11h00. The trip costs € 17 per person (roundtrip) and takes about half an hour. For the entrance of the site in Delos you pay € 6 per person. Boats return to Mykonos at 12h15, 13h30 and 15h00. In bad weather conditions the excursion is cancelled.
TIP: On Monday, the site of Delos is closed.
Consult here the transportation options from the cruise port to the city center of Mykonos.