Ischia is well-served by a network of small public buses. In Ischia Porto the bus station is just uphill from the port (above the junction dominated by a tall tree), not far from the hydrofoil terminal (from the big car-ferries you'll need to walk around the port to your left). Buses line up along the road before
setting off in various directions to the villages and towns on the island. There's a kiosk where you can buy tickets, which are valid for fixed time-periods. A single ticket costs €1.20 for 90 minutes' travel, and a two-day ticket is €6. Remember to stamp your ticket in the machine onboard at the beginning of your first journey.
One useful service is the number 7 bus, which runs from Ischia Porto to Ischia Ponte; a short journey of around ten minutes. The CD and the CS are handy for sightseeing, if you catch them at a quiet time of day. They both circle the island - the CD goes clockwise and the CS counter clockwise. Between Ischia Porto and Sant'Angelo the route follows winding inland roads high in the hills, with spectacular views. From Sant'Angelo the way is speedier, calling in at the other coastal towns.
Taxis are easy to find in Ischia, with plenty hanging around the port and other busy areas. Some are normal cars, but others are milk-float style microtaxis; entertaining little open vehicles with awnings.
From the ports you can take various boat tours and trips around the islands, advertised by big signs around the water's edge. Small water taxi services will also take you along the coast to less accessible beaches and sights.