Where to begin? Electronic ignitions come in many shapes and sizes using different technologies. Some use a light trigger and others use a magnet or steel reluctor passing a pickup/sensor.
The principle is the same in all systems in that a trigger sends a signal which end up as a spark from the coils. Some use a 12v battery and others are self generating like an old school magneto (race only). They are most accurate if triggered from the crank, but on most old bikes, that isn't an easy option for a street bike, so they typically mount on the cam instead replacing the points and points cam.
The two major tasks in adapting one are modifying the rotor to replace the points cam and modifying a backing plate to mount the pickups. It's all fairly simple once you are familiar with points and ignitions in general.
CB350 Specific
Newtronics make , or used to offer a light based unit for the CB. They are based in the UK.
Electrexworld in the UK/ HPI.be out of Belgium, offer a race only self generating CDI system which is very popular in Europe
Rex Caunt used to offer a PVL based self generating race ignition system
Boretech in OH offer a version which simply replaces the whole points assembly and uses the rest of the normal OEM electrical system.
NON CB350 Specific but can be adapted.
DYNA: the DYNA S for a GL1000 is easy to adapt to fit any Honda twin with OHC. You could also take any 4 cylinder system and remove the triggers from the backing plate and fit them to a slightly modified CB points plate.
Pertronix: Beloved by CB160 racers and hated by almost everyone else, it's a car based pickup which I have zero experience with.
Ignitech: Modern programmable system that requires some fabrication skills to work out a mounting system. Great system but probably not for the uninitiated.
In the US, the easiest is probably BoreTech. Bill Moeller who is/runs BT is a straight shooter and seems to know what he's doing and has been around for a while. I have not used one of his, but they have a good reputation.
The real advantage of an electronic system is the lack of things to wear out or go out of adjustment. Having a stronger spark is the icing on the cake. Points work fine. I raced for years with a modified points system and that was OK but I would not repeat that now that there are so many options. But for the street, a clean set of well adjusted points works fine.
When cash is tight and we're talking street not track, I'd recommend new points and condenser if they are needed plus a coil off ebay if that's needed, but I'd start by cleaning every contact and ground in the electrical system first starting with the kill switch and the main switch.