A zener diode in conducting state acts like a normal diode. It's the reverse voltage that distinguishes a zener diode from a regular diode. Take a look at the picture below.

In this picture you see a reverse connected zener diode. The 'value' of a zener diode is given in volts; this is the reverse voltage. But a zener diode doesn't blow when the voltage tends to get higher. A zener diode stabilizes the voltage at the reverse voltage. So the voltage across the zener diode in the picture above will always be 4.7 volts, even when the battery voltage increases.

Again, we need to calculate the value of R1. Unfortunately, it's difficult to say what's the ideal current flow in a zener diode. (Yep, altough the diode is reverse biased, there is a current flow!) In most cases 5mA is fine. Since the voltage across R1 will be 9V-4.7V = 4.3V, a good value of R1 is 4.3V/5mA = 860Ω.

A zener diode manufacturer publishes the maximum power dissipation of a zener diode. 0.4 or 0.5W is a very common value for a small zener diode. Using this characteristic, we can calculate the minimum value of R1: Assume we use a 0.4W zener in the design above. Since the voltage across the zener is 4.7V, the maximum current flow is 0.4W/4.7V = 85mA. The voltage across R1 will be 9V - 4.7V = 4.3V. So the minimum value for R1 is 4.3V/85mA = 51Ω. So a good value of R1 ranges from 51 to 860Ω. 820Ω is a good choice. Note however that the calculations above only count for a zener without a load. Take a look at the picture below.

In this design zener D1 has a 50Ω load (R2). Again, we'll calculate
a proper value for R1. Since the voltage across the load R2 is always
4.7V, the current flow in R2 will always be 4.7V/50 = 94mA. The current
flow in D1 should be between 5 and 85mA. So the current flow in R1 ranges
from 99 to 179mA. The voltage across R1 is always 4.3V, so the resistance
should be between 24 and 43Ω. 39Ω may be a good choice. In that case, the
power dissipation is 4.3^{2}/39 = 0.47W. So you'd
better take a 1W resistor!

But what should we do if the 50Ω load can be detached, e.g. because
it's an external load? With the load connected, the
*maximum* value of R1 is 43Ω, but without the load the
*minimum* value is 51Ω!

The answer is simple: use a higher wattage zener diode, e.g. 1.3W. In that case, the maximum current flow in D1 is 1.3W/4.7V = 276mA. This means, without the load connected, a minimum value of R1 of 4.3V/276mA = 16Ω. Now we have an overlapping range of values for R1 from which you may choose one. Again, a 39Ω/1W resistor is a good choice.