Oh man I once left my airbrush soaking in Medea Cleaner, which I thought would be a good idea... but it turns into a honey resin/tar type stuff when it dries ugh...
Anyway it depends on the nozzle. If it's really small you might be best going some sort of soak / chemical / ultrasonic route, otherwise I use these types of tools:
This is the Mack kit, the blue thing with all the steel rods is my goto:
https://www.ebay.com/p/?iid=391377090217&&&chn=ps
This is the H&S nozzle cleaner, good too:
http://www.chicagoairbrushsupply.com/noclne.html