How does a pilot follow a holding pattern? Do pilots have to manually change heading and altitude (through the autopilot) each time they are making a turn? Or is it something the Flight Management Computer (FMC) can handle?
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Generally speaking the Flight Management Computer supports holding patterns. The pilot inputs the holding fix (usually a NDB/VOR), the direction of the hold (Left/Right), the inbound course, and the time/distance that one holding leg shall take to execute. These information can be found on aeronautical charts, as IFR holding patterns are published for each airport. As far as I know pilots are also trained to fly holding patterns manually, but you can understand that flying the pattern manually is not as precise as flying the pattern via the autopilot.
air-traffic-controltag in your question but the question body has nothing to do with ATC. Also "How do holding patterns work?" is a very broad title that will call for a variety of answers. $\endgroup$