The airplane will be flown on autopilot for almost the entire trip, but not usually during take-off or landing. Most commercial airline flights are flown primarily under computer control, with the pilots simply keeping an eye on the computers. Since take-off and landing are the fun parts, pilots still prefer to fly these by hand, if weather conditions permit.
Take-off, in particular, is always flown by hand to some extent, although the computer is often allowed to handle the throttles (autothrottle).
Airliners can land easily under computer control, but pilots like to land, too, so usually landings are conducted by hand. In poor weather, radio-assisted approaches such as ILS are used to help the pilots align with the runways. Standard ILS does not land the aircraft, but just guides it most of the way down towards the runway. Cat III ILS, however, will guide the airplane all the way to touchdown, and it is used when visibility is so poor that virtually nothing can be seen outside the window. Pilots will use Cat III ILS (autoland) when visibility requires it and when the airport is equipped to handle this type of landing. Cat III helps reduce the need to divert to a different airport if the original destination is fogged in. Airports that have a lot of fog, such as Heathrow in London, or San Francisco, usually have one or more runways equipped for Cat III autoland.