Here is a paper describing various ways to make the phase noise measurement. Around page 30 it talks about delay line methods. Basically, to measure phase noise you need to downconvert your VCO signal with a local oscillator. One way to do that is to take a copy of your VCO's output, delay it in time long enough so it is no longer coherent with the present VCO output, and use it to downconvert to baseband.
You basically only need an amplifier (to boost the VCO signal in power), a power splitter, a long length of low loss cable (say 100 feet), a manual 0 to 360 degree phase shifter, and a mixer/10 Hz to 40 MHz video amp (part of the phase noise measurement stand if you have a preassembled one from HP, etc), and a low frequency spectrum analyzer. You turn the crank on the manual phase shifter until there is ~ 0 VDC coming out of the mixer, and then measure the AC part on the spectrum anlyzer. You then calibrate the spectrum analyzer output to dBc/Hz (using one of various methods) and have your answer.
Since you are using the VCO as its own local oscillator, you can make measurements even though the VCO is jumping around a lot.
Delay line frequency measurements are not that sensitive close to the carrier, and are useless at very high offsets from the carrier (because the delay line has a null in its transfer function at 1/τ)
tf.nist.gov/general/tn1337/Tn190.pdf