Zener diode in comparator

The way you've drawn it the zener diode clamps the power supply reducing the 34V to 12V. What's even worse is that there's no current limiting and the diode will be destroyed.

The zener diode needs a series resistor to take care of the voltage difference between the 34V and the 12V.

To calculate the resistor value you need to know how much current the zener diode needs and how much current should go into the load (the opamp in your drawing). Zener diodes are often specified at the rather high current of 50mA, though more modern types will work properly at current less than 1mA. (This one only needs 50\$\mu\$A.) Let's suppose it needs 10mA and that the opamp will also consume 10mA, that's a total of 20mA. That's the current through the resistor. Since we already know the voltage across the resistor Ohm's Law will give us the value:

\$ R = \dfrac{\Delta V}{I} = \dfrac{34V - 12V}{20mA} = 1100\Omega \$

If you check the power dissipated in the resistor (something you always should do) you'll see that this is 0.44W, so use a 0.5W power resistor.

edit
My original answer talked about 50mA zener current. That's very high, and I also realized that at 50mA a 12V/400mA zener would operate out of spec, as also jippie pointed out. It appears that the high current is only used for lower voltages (76mA for the 3.3V 1N4728A), and at 12V the datasheet talks about a safer value of 20mA. It's OK to use a lower current, though load and line regulation will be worse.

1. A transistor is a different type of (active) component entirely, to a passive component such as a resistor/capacitor/inductor. They have many different characteristics listed in the datasheet, one of the most important being current gain. If you don't understand much about them I suggest you get hold of a decent introductory electronics book and read up about them. There are thousands of part numbers, but in many cases you could use many different options. In a circuit such as this most general purpose NPN transistors will do (2N2222, 2N3904, BC337. etc)

2. The zener appears to be used in order to ensure the voltage does not rise above 3.3V (the zener will start conducting above this voltage) thereby protecting the 3V phone input from overvoltage. You don't need to calculate this value, you simply need a 3.3V rated zener, of which there will be many part numbers to choose from (assuming this is what the circuit requires)

EDIT - regarding more detail on why the transistors can be swapped, it's hard to explain briefly. They do have similar specifications, and are available in the common and easy to use through hole TO-92 package. The circuit shown is not ideal, but for a rough shifting circuit it will probably work with some distortion (how well depends somewhat on the input signals DC bias level)
Since important parameters like current gain can vary widely with temperature and between parts of the same number, a good transistor circuit will not rely on these parameters but control them with some basic feedback (e.g. by using an emitter resistor in a common emitter circuit)
Any good electronics book will have a section on how to use a transistor, understand it's parameters and design a circuit that meets your specifications with them. The website All About Circuits is pretty good (see section 3 for semiconductors), and book wise this question and it's answers should be of use: Basic Electronics Book. With a few hours of reading and a couple of breadboard experiments you should begin to see things more clearly.