All takeoffs and most landing are done manually. In reduced visibility conditions, many airliners utilize auto land where the autopilot(s) perform the landing under the close monitoring of the pilots.
One way to tell if an airport has ILS or not (assuming you can't discern from the cones), is to tap on the airport and then go to the “runway” heading. If you tap on a specific runway and the “set NAV 1” button is disabled, then that runway is not equipped with ILS.