Turn the circuit breaker off. Allow ten minutes for built-up charge to dissipate.
Touch a metal object to remove any built-up static charge you have.
Locate the light switch you want to test and unscrew the switch plate.
Look at the switch wiring to see if any wiring or contact points are charred. There should be one wire coming from each terminal of the switch.
If this wiring has come loose or is touching the metal box instead of making contact with the switch terminal, a short circuit will result and overload the breaker.
Replace the switch cover if everything looks as it should.
Access the outside light fixture if possible and remove the light bulb. Unscrew the fixture cover and inspect the wiring and contact points as you did with the switch.
If you see no problems here, replace the fixture. The problem is elsewhere along the circuit and you'll need a certified electrician to check it.
Ensure the outside light switch is off and restore power to the circuit. Avoid using that light until you get the circuit checked and repaired.