From Naples Airport you first have to reach the center of Naples, there are different buses connecting tha airport to the city and you can find it here: Naples Airport Connections .
To reach Crotone there is a ride per day from Naples, leaving from Naples Piazza Garibaldi at 5.00 pm and arriving in Crotone, at 11 pm. The company is called Autolinee Romano.
For more information check Autolinee Romano Interregionali