By train is the obvious choice. The Cattolica-San Giovanni-Gabicce station, just inland from the centre, is on the main Adriatic line between Bologna and Ancona. Trains run hourly or better from Bologna (about 1h 45m), Rimini (10 minutes), Pesaro (10 minutes) and Ancona (45 minutes), with through services from Milan, Venice and Rome.
By car, the A14 motorway runs parallel to the coast; take the Cattolica exit and follow signs for the centro. Driving in town is straightforward outside July and August; in peak season, expect heavy traffic and pay-to-park.
By air, the closest airports are Rimini Federico Fellini (20 minutes) and Ancona Falconara (50 minutes), both with seasonal European budget flights. Bologna is bigger and 2 hours by train.