Sure thing.
I'm not sure if I'm allowed to share a link on this forum. Anyways, here is a link, but below is also my summary of what I've learned.
About using a vector network analyzer (VNA) - Page 1
As I understand the answer (and correct me if I'm wrong), the VNA in this configuration (1 port measurement, S11) is supposed to be the only signal source.
First and foremost, the VNA has to be calibrated with an open, short, and 50 Ohm load (also refered to as calibration standards, or collectively a calibration kit). This is because the VNA will also look at the phase angle between voltage and current, so it can tell you if the load is inductive or capacitive, an by how much. When the device under test (DUT) is not perfectly matched, there will be reflections, creating a standing wave. This will look different depending on how long the cables are. So for example a capacitive load may look like an inductive load just by adjusting the length of the cable. This is the reason why calibration is so important. The VNA will calibrate out the cables, so that once the DUT is measured, you are really only seeing that and everything in between the DUT and VNA is canceled away. The end of the connector that hooks up to the DUT is also called the reference plane.
One thing that doesn't depend on cable length is the VSWR, which is also an indication how good the match is. My colleague is probably just looking at the VSWR in some way. So while he's definitely doing things wrong, it's not to say that he doesn't get some meaningful information out of it.
It's definitely ill advised to be sending RF power into the VNA. In my case the maximum allowed is 26dBm, while the DUT was transmitting at 28dBm. This is bad but in my case it wasn't enough to destroy this super expensive piece of equipment. When using it in this way, at the very least he needs to use an attenuator to protect the VNA (which of course would also need to be calibrated out).
Someone also said to look up ["Hot S22" measurement, where you try to measure S22 of a power amplifier with a large signal coming out of it].
One thing that really helped me understand the subject was learning how the smith chart worked, both the impedance side AND the admittance side. Admittance is used when using components (capacitor/inductor) in parallel, and the impedance side is used when using components in series. By mixing and matching these components, one can match an impedance to anything.
For example on the smith chart, the left-most point on the circle is a short and the right-most point on the circle is an open. If for example I insert a parallel inductor, if I start with a really big one, it won't really have any effect, but as I make the inductor smaller, it will start to let more current through (to ground), so the impedance will move towards the short (left). If instead I'm inserting a very large capacitor in series, it won't do anything at first, but as I make the capacitor smaller, the impedance will start moving towards the open (right side). It's interesting how the point (impedance) moves about the smith chart, and how you can control it. All this doesn't even really require any math, which is great. Also any point you put on the smith chart is only valid for one given frequency.