Asking just out of curiosity. What modifications need to be made on an engine, e.g. Lycoming O-360, that normally uses AVGAS to utilize it with MOGAS?
STC aside, no physical modifications are required to an engine to run on Mogas (except possibly the fuel system - see below). My Lycoming O-290 has been using it for 9 years with no issues, and in fact the engine is FAR happier on Mogas than 100 LL, which low compression engines are unable to lead scavenge adequately and require frequent plug cleaning and are prone to exhaust valve sticking from lead buildup on valve stems (on engines meant for 80 octane).
The only benefit to running an 80 octane engine on avgas is a lubrication benefit to valve seats due to oxidized compounds that form with leaded fuel, and I will put some avgas in from time to time (there is a sliding action on the valve seat as the valve centers itself when closing - the lubrication effect reduces seat wear from this sliding).
One interesting effect is when I borescope my cylinders at annual, the exhaust valves are uniform off-white like they are in car engines, from the ash deposits unique to Mogas (on avgas, exhaust valves have a reddish bullseye pattern from the heating of the valve). You also get more soot in the exhaust instead of grey lead deposits.
The main potential issue is with the fuel system related to temperature and Mogas's higher vapour pressure (lower boiling point). If your plane has a fuel pump and it gets really hot under your cowling, it's strongly recommended to add a cooling shroud for the fuel pump (I recently added one to my plane to alleviate problems in really hot weather, where I could tell I was getting fuel pressure fluctuations after landing). It's a bigger problem for fuel pump systems than gravity feed because the pump's suction is effectively raising the altitude, as far as the fuel being pulled into the pump is concerned, and the fuel will boil more readily at the pump inlet. Gravity feed doesn't have this problem.
You can actually run high compression 100 Octane non-turbo Lycs like the O-360 on Mogas (I was in a glider club with thousands of hour operation on it with O-360s) and there is no issue with detonation, and in Canada you can even run engines like the supercharged R-985 on Mogas, on commercial operations even (some bush operators use it).
The above assumes the fuel is alcohol free. You can't legally use car gas with ethanol under the STC anyway, and if you have a homebuilt where you can use whatever you want, and want to use fuel with ethanol, then you have to make sure that all the rubber components in the fuel system, including the carburetor float valve seal, are alcohol compatible. This is possible to do.
Finally, if you are getting Mogas yourself from a gas station, make sure it is alcohol free and test it yourself (a simple test using water) to confirm it is alcohol free. If you're buying it from an airport, that's not a problem.
For any certificated aircraft engine, the type certificate will specify the required fuel. If the TC specifies AVGAS, using MOGAS will require an STC for that engine.
Developing a MOGAS STC for an engine is a complicated and expensive effort, so you're realistically limited to purchasing the rights to an existing STC. If there isn't an STC for your engine, you're likely out of luck.
Once you purchase the STC, it will include the installation instructions outlining the necessary modifications for your engine. In many cases, it's nothing more than placards and a flight manual supplement.