[Ecky]

I can think of a few possible configurations:

Serial - Engine generating electricity as-needed (and off otherwise), powering an electric motor which sits on the rear differential. Advantages include being able to run the engine at a fixed (peak efficiency) RPM at full load, and turn it off otherwise. Disadvantages include losses from converting mechanical to electricity, and then back to mechanical, as well as losses from resistance in the battery. Also requires separate motors/generators. Examples in modern cars include the Accord Hybrid.

Parallel - Engine and electric motor are both capable of providing power to the wheels. Civic Hybrid, Prius, Chevy Volt use this system. Direct drive avoids conversion losses, but without a CVT with wide gearing, you risk running the engine at low load and at varying RPM. Honda's electric motor is next to the flywheel, between the engine and the transmission, which has a disadvantage of not being able to run on electricity alone. All of them have the electric motor before the transmission, meaning there are some drivetrain losses that could be avoided. This method is often used like a turbo, allowing the engine to be downsized significantly, with passing and accelerating power being provided by electric "boost". Allows for the removal of an alternator, and is probably the most simple system to add onto an existing drivetrain. Would be a great to use in combination with a swap to a smaller motor.

AWD - Engine powering two wheels, electric motors powering two wheels. This is starting to appear in hybrid sports cars. Allows for more power than a series hybrid and gives AWD/4WD, but is more complex because it requires a traditional transmission in addition to having separate motors/generators.