Ragusa has no railway connection to Catania or Palermo — the branch lines that once served southeastern Sicily are gone. The practical options are bus or car. AST and FlixBus run coaches from Catania (journey time around 2.5 hours). From Palermo the journey is around 4 hours by bus.
By car, Ragusa is about 100 km from Catania and 275 km from Palermo. The roads across the Iblean plateau are scenic but winding. Catania Fontanarossa is the most convenient airport, with good connections across Europe.
Within the city, a car is useful but not essential if you are staying in or near Ibla. Parking above Ibla is free at the Parcheggio Giovanni Tumino; a steep path and stairway lead down into the old town from there.