How to connect the 0 ohm high or low
You need two resistors on each pin that needs to be configurable.
One resistor to the positive supply and one to ground.
Populate one or the other but not both with zero Ohm resistors. If you populate both you will short circuit the power supply.
You could also populate the pull-up resistor permanently with a relatively high value, e.g. 10kohms, then populate the pull-down with a zero-ohm resistor to set a logic zero. This approach would have a slightly higher power consumption which may or may not be significant. This approach is often used if a shorting jumper is used (as on disk drives for example) rather than soldering a component - only a two-pin jumper is needed; Leave out for high, insert for a low.
Often in designs intended to be automatically tested a small value other than zero ohms will be used, e.g. 220 ohms. This will work just as well to set the logic value in normal use but allows the test equipment to overdrive the selected logic value for testing.