By train, take any northbound train from the station (don't take from the Gatwick Express, or any train destined for Reading) and get off at East Croydon.
Croydon to Gatwick. About 14 miles.
take a bus.
About 17-18 miles following A23 & M23.
The train from Gatwick Airport to East Croydon Station would take about 20 minutes.