Modica is in the South-East corner of Sicily, at a distance of about 15 km from Ragusa and 125 km from Catania.
PLANE
Although in Sicily there are 4 airports, the best solution to reach Modica is the Catania Airport "Fontanarossa", which is connected to many Italian and international airports by frequent flights operated by several airlines.
Offical website of Catania Airport "Fontanarossa": https://www.aeroporto.catania.it/en/
HOW TO REACH MODICA FROM CATANIA AIRPORT "FONTANAROSSA"
BUS
Outside the "Fontanarossa" airport (arrival level), about 30 m on the right side, you will find an AST bus stop. AST is one of the most important public transportation company in Sicily. Each day, there are several rides from Catania Airport to Modica, about every 2 hours. The first run is at 09:15, while the last one is at 20:45, except on Sunday, when there is only one ride at 20:45. Detailed information about the bus departure schedule can be found at this webpage (sorry, there is only the Italian version). Be careful to select "CATANIA AEROPORTO" in the "Località di partenza" drop-down menu, while "MODICA" in the "Località di arrivo" drop-down menu. The travel time is approximately 2 hours and the fare is about 10 €.
CAR
There is also the possibility to reach Modica by car. The distance is about 125 km and the travel time is approximately 2 hours. Outside the "Fontanarossa" airport there are a lot of car rental shops.