Plugging an LED directly into a Duemilanove like you have is a good way of destroying the output pin, its completely unnecessary as the Duemilanove already has an LED on pin 13 built onto the board.
That old tutorial from the NG days wants either updating or erasing.....
The audio output from a walkie talkie is almost certainly negative relative to ground at times (like half the time) which means you won't be doing the ADC any good either. The analog input pins are 0-5v only (Not strictly but at this stage of the game, its near enough)
I'd do a bit of learning before you destroy your Arduino.
And measuring anything always involves making two connections, one is the signal you wish to measure and the other is a common reference connection usually called ground or circuit common. On a Arduino it's called ground and it needs to be connected to the negative side of the battery powered device you are trying to measure.
If the 'output' jack you are measuring is the RF (or antenna connection) of the set, you will never get anything meaningful to read on the Arduino, it's too high a frequency and is a AC voltage.
Without external components, anything wired directly to an Arduino analog input pin must be DC and not go above or beyond 0 to +5vdc.
I read it in a book I bought together with the Arduino.
If its telling you to connect an LED directly between Gnd and Pin 13, its way out of date. At one time in the Arduino's history it was OK to do it, not with modern ones like the Duemilanove since they don't have an inline current limiting resistor. What they do have is their own LED with resistor on Pin 13. (Usually marked 'L').
It depends on what you want to do with the audio and at what levels its coming out of the jack at. The arduino lacks horsepower for sampling audio frequencies so what you can do with it is a little limited. One way or another you need to get its output to 0-5v. It wants amplifying before rectifying so the 0.6 volt drop across a rectifier diode isn't so relevant then maybe reduce it with a voltage divider. Depends on what voltage is coming out.......
And you need to connect the arduino ground(Gnd) to the ground of the walkie talkie, if the idea is to digitalize the sound I don't think that it would work very well.
I sometimes find it handy to plug an LED in like that to test things - you can purchase a LED that has the current limiting resistor, suitable for 5v built in.