Let's see... my MiTo has a modern fuel-injected engine, so the ECU can basically rev the engine at whatever RPM it wants to (the accelerator in modern cars is merely a sensor input on the ECU, and isn't physically linked to the engine). That takes care of power and acceleration. Then there's traction control, so there's hardware in the car capable of electronically applying the brakes and so the car can theoretically stop on its own. Finally the power steering is electronic, not hydraulic, so the necessary motors for that are already present.
My MiTo only uses this in a limited fashion. The ECU will decrease the revs if it detects both front wheels are slipping. Interestingly it will also increase revs to avoid wheel slip - if I downshift aggressively it will demand more torque to stop the wheels sliding from turning too slowly. As for braking, switching the car to D mode (there's a switch that can be in All-weather, Normal or Dynamic mode) enables an electronic differential which simulates a mechanical limited slip diff by braking one of the front wheels - this is on top of the standard electronic stability control (Alfa calls it VDC) which can brake individual wheels to correct over/understeer and skidding. The power steering however doesn't do anything fancy, though switching to D mode apparently makes it feel sportier.
To be honest I've not tried D mode yet - it also comes with a more aggressive throttle response so I think I want to be in very light traffic the first time I try it lest I launch myself into the car in front. Besides, in the non-turbocharged engine I've got there's no difference in horsepower between the three modes (in turbocharged MiTos, D mode increases the boost pressure).
Anyway, back to self-driving. There's still the issue of the gearbox - here it's a manual gearbox so someone would have to start the car and handle gear changing. If we start playing with optional extras though then it changes as one option is a semi-automatic transmission, which is essentially a robotic gearbox and clutch (on the MiTo it's a dual-clutch system with separate gearboxes for odd and even gears to get faster gear changes). At that point the car can and does change gear all on its own. Add in start/stop (standard on the Multiair variants) and now it could start itself. The handbrake is still manual, but you could work around it by leaving it in gear when parked.
It still doesn't know where it is or what's around it, unless you add even more options. There's Blue&Me which is an integrated satnav, although that's not as useful as it might appear as a realistic accuracy for civilian GPS is about 10 metres... on a good day (Galileo will eventually help this by increasing accuracy to 1m). Next there's parking sonar which is available in both rear- and front-facing options, and with that the car could sense something like a wall in front of it. And that's it for the MiTo - putting everything together so far would get something that could follow a path of GPS waypoints and probably wouldn't hit anything big in front of it. Certainly it's not something that could be let loose on the roads! To get to true self-driving would need more hardware, though at this point it's just sensors and (lots of) processing power that's missing.