At most airlines the the Captain and First Officer swap each leg in terms of who is the "Flying Pilot" and who is the "Non Flying Pilot". The flying pilots obviously flies, and the Non does everything else, radios, gear, flaps, PA's, etc.
In large aircraft the Capt taxi's with the tiller on the ground, then usually at a predetermined speed on the take-off roll the controls are transferd to the First Officer if s/he is the flying pilot, and then the same applies on landing, once the aircraft is slowed to a predetermined speed. This is all spelled out in the each airlines operations manual.
Some airlines have requirements that the Capt has to do the take-off and landing in certain situations. The airline I work for, until you have 100hrs in the aircraft, the Capt is "supposed" to do the take and landing in, vis less than 1 mile, cross wind greater than 15 knots, braking action less than fair, when windshear is reported, at special use airports. This limitation is removed after the 100hrs is reached or about 1 month of flying.