The North Atlantic (NAT-HLA) High Level Airspace is special use airspace where a series of optimized routes called the OTS, Organized Track System, are published every day, twice a day. This airspace is unique for having a largely unidirectional flow of traffic, and the waypoints to be followed over the Ocean are not fixed. Your assumption "following the jet stream" is part of the answer and the following 2 extracts from ICAO NAT-HLA Doc. 007 should effectively serve as a more complete answer to that question.
2.1.1 As a result of passenger demand, time zone differences and airport noise restrictions, much of the North Atlantic (NAT) air traffic contributes to two major alternating flows: a westbound flow departing Europe in the morning, and an eastbound flow departing North America in the evening [...]
2.2.1 The appropriate OACC constructs the OTS after determination of basic minimum time tracks; with due consideration of airlines' preferred routes and taking into account airspace restrictions such as danger areas and military airspace reservations. The night-time OTS is produced by Gander OACC and the day-time OTS by Shanwick OACC (Prestwick) [...]
The routes actually flown are created by the company Flight Dispatcher and provided to flight crew as an "Operational Flight Plan" or OFP in paper or digital format. This plan is sometimes called a Fuel plan because it determines the legal minimum fuel required. Most of the time it represents the most fuel efficient routing but it can also be set up for time efficient routing or routing manually strung up by the Dispatcher etc. Overflight charges (fees) are also factored into the cost optimization. For longer flights especially, a 'route search' is carried out as there maybe many route options available and an effective choice can result in much cost saving.
The Flight Planned route and other details are fed to the on board FMC (Flight management Computer) either manually by the pilots in case of a paper flight plan or, the plan can be up-linked by the Dispatch office using electronic means, and checked, accepted and activated by the pilots in the cockpit with a few button presses. Capability exists today for the pilots to accept route change suggestions by Flight Dispatch whilst enroute in real-time thanks to realtime monitoring of the flight progress and weather/wind conditions and subject to ATC clearance.
At the current state-of-the art, and with increasingly reliable datalink capabilities, the grunt work of optimal flight planning is left to a specialist Flight Dispatcher and sophisticated flight planning software. Comparatively, the on board FMC can do rudimentary optimization with respect to winds aloft as it only knows the limited wind forecast fed in by the pilot or uplinked from Flight Dispatch. The Autopilot/FMC combo can fly a given route, but it cannot create that route.
And Yes, the auto-flight system's normal mode is to couple the autopilot to the flight plan loaded into the FMC, infact this is the way most of the navigation is done in today's airplanes.
Finally, some points on GC flying -
- 'minimum distance' (=Great Circle) is one of many factors upon which flight planning is dependent.
- The internal FMC navigation functionality is such that it strings and flies each segment between waypoints as a Great Circle.
- If ATC was able to allow free, 'point to point' routing from the departure direct to destination, it would be one GC track all the way.
- What also hinders us, is the fact that we have to follow Airways, and traditionally, Airways were from radio beacon to radio beacon, and beacons were located at airfields and towns/cities and these were rarely coincident with the GC.
- Flights over the oceans and other remote areas may have a better chance of conforming more closely to the corresponding GC.
- ATC already clears us for "direct" routings at the tactical level, in real time. Their concern for a green world is the same as our's!
- Despite being an oceanic area, NAT flights are more rigid about maintaining the planned (non-GC) route and they aren't able to agree to many direct routing requests because of the nature of the operation, in turn dictated by the sheer volume of traffic and it's mostly unidirectional flow.
- Todays Flight plans can even give us niceties like a Great Circle Index or GCI which tells us in percentage form how much more distance we are flying compared to the direct GC (though this info may not be of much practical use in light of the more sophisticated optimization mentioned above).