What actual engine modifications are required to allow certificated piston engined general aviation aircraft to run automotive fuel under an FAA Supplemental Type Certificate (STC)?
For most engines it would require a hardened valve seat.
The reason why lead is required for aviation engines is that the value seats are not hardened and the lead in the gas helps prevent "micro-welding" that can occur on a valve seat. Micro-welding happens when the valves are hot and the the valve is pressed against the valve seat; the valve will start to weld to the seat before it is torn away when the valve opens. This causes a jagged edge at the valve seat which causes a bad valve seal. Old engines relied on the lead in the gas to prevent this. When the automotive industry switched to unleaded gas, the engine makers had to use valve seats out of hardened materials that were more resistant against heat.
The lead is also a great octane booster although many airplane engines can use octanes lower than 100. In automotive fuels today ethanol is used to boost octane and that has its own host of problems since ethanol is very corrosive. So before you switch to automotive fuels you need to make sure you engine and fuel system can handle the ethanol.
For a discussion of micro welding among mechanics check this link out.
EDIT: After doing more research I discovered that Lycoming has always used hardened valve seats so the modifications on a Lycoming engine would be very minimal. However, most Continental engines do not have hardened seats and major modifications would be required.
Lycoming has a good article on the use of unleaded fuel in the their engines here. Notice however that Lycoming states that ethanol CANNOT be used in their engines. In the US at least it is getting very hard to find fuel that does not contain ethanol.