What do you want to convert?
What I mean is, do you want to convert the entire car including the engine (ignition coil, distributor points, etc.), or only the accessories (e.g., radio, bulbs for lighting, etc.)?

If it's the engine, this will be hardest. You'll probably have to look into cobbling 12-volt stuff to work in your car -- for example, a new ignition coil and distributor points/condenser (putting 12 v into a coil designed for 6 will cook it; same for points). Some earlier 12-v cars had a resistor to reduce amperage to those components: during start-up when the starter was spinning, they got a full, "12 volt" equivalent shock for a hot spark, then for running the resistor was in the circuit to limit current. If you can't change those parts, you may have to resort to some resistor like that. Consider a modern, solid-state ignition, too, so you don't have to redo your points every few thousand miles.

As for the car body's accessories (radio and lights), there are converters available (try hot-rod shops). The fuse bus for these things will be fed through the converter.

The remaining problem will be certain gauges -- maybe the temp and fuel gauge -- which will be relatively easy to solve. They're usually (I don't know about your car specifically) designed to work off a constant voltage (via a regulator, electromechanical, this being on car predating solid-state electronics) source slightly below ordinary battery voltage, in order to show reliable readings: maybe at 4.5 or 5 volts (just guessing) vs your car's original 6+ volts. You will have to find the specs for the original voltage "regulator", and then you can easily match this with a modern solid-state (discrete chip) voltage regulator of that same, low voltage, rating to keep them accurate.

Good luck.