It's implied that the Enterprise bridge crew, in any of the TV series, spend long durations at their duty stations, either sitting or standing.
What exactly are they doing for hours on end while the Enterprise is en route between destinations? Is it me or does this seem like an incredibly tedious if not fatiguing job, sitting in a chair staring at the same view screen? Couldn't these tasks be automated?
There's more automation on the TNG era shows than in the TOS era. There is still plenty to do, though.
In the TNG era, the Conn officer (Wesley Crusher) constantly checks the course and adjusts it as necessary. the Tactical officer (Tasha Yar, Worf) scans for possible threats even in normal flight. The Ops officer (Data) allocates ship resources for mission requirements. The stations at the rear of the bridge are for more specific usages. There are two science stations for performing scientific research (What Spock's station on TOS). Mission Ops is a bit more detailed than regular ops. The bridge Engineering station is an excuse to get Geordi LaForge on the bridge for dialog. There was also a control station for the Environmental systems. Any computer station can be reconfigured to do any job.
Some extras just seem to be hanging around in case one of the main cast members need to beam down. I'm sure that the writers could come up with their duties if they needed to do so. Just as a real world Navy ship is going to have people doing duties on the bridge at all times when underway, so too will fictional ones.
I am an ex-military Navy crewman so I will try and use that experience to extrapolate what crew members on the bridge of a ship might be doing. A military vessel underway is never at rest. Crew members need constant training and cross-training (in the event of the death of primary officers or technicians) engines need tending, crews need feeding, equipment needs cleaning and maintenance, and even a ship as vast as the Enterprise will need enough crew both to care for the ship and for each other.
Understand, automation can handle many of the duties performed by human crews today (such as cleaning and basic support services) but with the increased complexity of technology, there are still many places which should still have human oversight, interpretation and coordination.
On a starship doing less, there is the possibility of running a ship with a smaller crew. But the crew is not there specifically for when the ship is doing well and capable of automating many of the possible decisions necessary for it to function.
The crew is there for when circumstances are no longer perfect and a human is needed to make decisions, perform operations, work-arounds, juryrigs and other means of making a means when technology cannot do it alone.
NOTE: Ships like the Dreadnought featured in the Abramverse Star Trek: Into Darkness, with a minimal crew were probably built on the Borg ship premise of multiple redundant systems allowing the ship to function with a minimal crew but exclusively as a warship. It would have also been part of a fleet of ships providing whatever intelligence was necessary for it to complete its mission.
On a humanely run ship, the workday is probably still broken into shifts ensuring no crew member works more than a reasonable number of hours a day (probably 6-8) giving crew members enough time for rest and continued professional development.
While on duty, most bridge crew members are engaged in monitoring whatever services they will need to be available during a time of increased activity or under an alert status.
Engineering, for example, having such a huge responsibility for maintaining primary power for operations, weapons and life-support will be engaged in training, preparations, security, and safety of the matter-antimatter engines and related systems. The engineering aspect of a Federation starship is central to almost any effective operations of said vessel. In addition, the maintenance and integration of secondary systems such as the impulse engines and non-warp auxiliary power is absolutely vital when primary power is offline.
Communications, probably a smaller division on a starship still has to coordinate orders from Starfleet, monitor local communications traffic for star systems and starships nearby in case of military threat or incursion, medical emergencies or diplomatic operations. Even in an era with universal translation, I suspect language facility, training, social and political scientific training fall under the province of Communications. Communications also supports internal teams for damage control and internal security.
Helm Officers, more than likely are involved in monitoring maintenance of sensory systems related to helm control, integrating power management and control system used to navigate, triangulate and target enemy vessels in coordination with the Tactical and Science stations.
Tactical Officers are coordinating combat training, drills, and security operations dealing with operations and alert status. They will be maintaining internal security, force fields operations, and repair party operations in coordination with Communications. On duty, their jobs probably include the continual monitoring of local ship traffic, long distance scanning for possible enemy ships or anomalies.
Science Officers spend their time supporting and prioritizing scientific procedures common to starship operations. This may include monitoring and improving sensor capacities, refining alignment of sensors for increasing resolution and accuracy.
I suspect Federation starships are just like real Naval ships, beehives of preparation and training for the inevitable confrontations, scientific investigation, and unexpected circumstances of a ship engaging in active interstellar exploration of a highly-populated galaxy.
