The two terminals are joined by a free, driverless shuttle train. Follow the signs for the other terminal.
How long it takes
The ride takes about two minutes and the trains run every few minutes, day and night, according to several secondary sources. Gatwick's own page on this would not load, so confirm the hours. Allow about 15 minutes in all, including the walk to and from the stations.
If your hotel is at the other terminal
Gatwick says Hampton by Hilton is about five minutes from the South Terminal by the free shuttle. One third-party source puts the Hilton at about ten minutes from the North Terminal. Add the time to the stay's own walk.
Roads
Vehicles cannot drive between the terminals inside the airport. A taxi or transfer must drop you at the correct terminal.
From the railway station
The station is in the South Terminal. For the North Terminal, take the shuttle train from there.