On a FWD car, it is a right PITA, to the point of redifining PITA.
The throttle linkage is different, you end up having to do body work to put the new shifter in and rework the pedal mounting assembly, the engine management computer won't know what to do as it no longer has the proper input from the transmission as far as speed, torque, etc. The cooling system is different (autobox uses the engine's radiator for cooling), the differential will be much different, and most likely the exhaust will need to be moved to accomodate the different bell housing and transmission casing shapes.
It is a total engine-out transformation that will leave you without the car for SEVERAL weekends (if you do it yourself, which is the only option to make it financially worthwhile), and requires many tools that are specific to the job.
On a RWD car, it is only marginally easier due to the fact that it is not so much of an engine-out operation. But that's where the "easier" bit ends.
It's not so much of just a matter of swapping out the transmissions. The engine has to come out so that a new flywheel can be mounted and balanced (auto's don't so much use a flywheel as they have the torque converter for that, so thier "flywheel" is just a thin metal plate), the harmonic balancer can be removed from the front of the crank and the proper pulley installed, the throttle linkage modified, the cooling system swapped out with the proper one, the wiring harness and respective computers changed out, the extra hole drilled in the firewall for the clutch cable (OMG if it's a hydraulic clutch, even MORE problems), the transmission shifter hole made to fit correctly, the differential swapped out for the correct one, and the new exhaust put in. Then it's a matter of squeezing the engine back in and chasing down all the new faults (which there will be many).
If it was a classic car that ran on a carb, it almost IS a direct swap out. Pull the engine, change the flywheel (to hel with it as far as the harmonic balancer goes, leave it there), install the clutch lever and cable, sawz-all the shifter hole, drop the whole assembly back in and fire her up.
But I don't imagine your pride and joy is a 1984 or older Celica, is it? If not, then it is easier in time, money, effort, and all around hassle to change cars rather than transmissions. Even WITH all your new kit.