The exact process varies quite a bit from airport to airport and even sometimes from terminal to terminal within an airport. But assuming a relatively modern terminal at a relatively busy airport, most of the process is heavily automated to reduce both labor and error.
Bags will be taken by conveyor to a security station, where a human watches them pass through various scanners. Then they get sorted by machines onto belts going to various parts of the terminal, and then belts going to each gate. This is why bags all get a big white tag with one or more barcodes on it, connected to a database that (hopefully) knows where each barcode should be sent.
Once the bag arrives at the gate, a human will transfer it (just a few feet) from the belt either onto a baggage cart (for smaller planes) or into a Unit Load Device (for larger planes), where it then waits to be loaded onto the plane. Notably, all bags on the same cart or in the same ULD will be waiting for the same plane.
At the other end, a human transfers the bag from the cart or ULD onto to the belt, and it goes back up into the system to be scanned and sent either to a different gate or off to baggage claim.
A single baggage handler can't really change much. They could intentionally misload a bag on the wrong aircraft (heck, they do it often enough by accident), but that is only easy if the "right" aircraft were at the same gate, or at least near enough to move the bag without another handler noticing the odd behavior, and there's no guarantee they'd be assigned to that gate at the right time since baggage crews move around a terminal pretty fluidly as planes come and go. And the "mistake" would be quickly detected when the plane was unloaded at its destination, unless of course a handler there was part of the same conspiracy. Many airline employees have been caught smuggling drugs this way, and presumably many more haven't been caught, so it's completely realistic.
More practical for a true conspiracy, though, would be planting, bribing or blackmailing someone who can simply change the database that says where a particular barcode should go. There are systems that check to ensure a passenger and their luggage aren't separated, so you'd need to attach the bag to someone who you'd be certain wouldn't miss the flight, and then detach it at the other end so you didn't get caught.
Overall, it is a lot simpler to trick "the system" into unwittingly doing your nefarious work for you rather than having a grand conspiracy of humans trying to outwit said system. But it may not make as good of a story.