Halkidiki is reached almost exclusively from Thessaloniki — there is no airport on the peninsula itself. Thessaloniki airport (SKG) has international and domestic flights all year. From the airport, the simplest option is a hire car: it takes about 90 minutes to the start of Kassandra, two hours to the middle of Sithonia, and two and a half to Ouranoupoli.
KTEL buses run several times daily from Thessaloniki's Halkidiki bus terminal (separate from the main KTEL station) to all the main resort towns. Once you are on the peninsula, public transport is sparse — you will want a car or scooter to move between the three peninsulas.