I am assuming it is fuel injected, but a lot of this can apply to a carburated engine as well.
Since it ran dry, and since it is as old as it is, I'd first change the fuel filter. Once the fuel pump sucks air, that turbulence from the air can shake loose an amazing amount of debris from the fuel lines and wreak all kinds of havoc including fuel starvation.
With the fuel filter off, check the pump flow. Running the tank dry can also cause the filter sock on the inlet to collapse. Doing this will also insure that there isn't any air left in the line to cause a cold vapor lock. And it will indicate whether the pump is working ok.
Once you know you have good fuel flow, if it is still stalling, check the intake for a cracked inlet horn, disconnected hoses or cracked plastic fittings. A backfire through the intake can cause a long list of vacuum related issues that will cause stalling.
Those are the easy checks.
If all that fails, then you have an issue that will take some digging. You may have plugged injectors or carb jets, messed up sensors, blown intake or head gasket or other problems that can crop up from running out of gas.
