1.) RF Gain
Use a generator and a RF power meter. Both must have the same impedance as the device being tested which is typically 50 ohms at microwave frequencies and 50 or 75 ohms at lower frequencies. The power level must be below (eg >10dB below) the maximum the device can handle else it will be compressed. At each frequency measure the power out of the generator, then connect the device, and measure the amount of power out of it. Pout - Pin = gain A network analyzer or vector network analyzer (VNA) can be used and is more convenient and faster but is still based on Pout-Pin = Gain.
Example: Pout = +5dBm, Pin (from the generator) = -15dBm then the gain is [Pout - Pin] = [+5dBm - -15dBm] = 20dB gain Note gain is relative and expressed in dB, not dBm which is power in dB relative to 1mw. (eg 1mw = 0dBm)
2.) Gain Flatness
The gain flatness is the difference in gain for a device at the different frequencies measure in 1 above.
3.) Gain Matching
Gain matching assumes you have measured 2 or more device using the technique described in 1 above. You then compare the measured gain of the devices at each frequency.
(question 4 was two questions and have been divided into 4 and 4a -hms)
4.) Return Loss
Using a direction coupler or bridge you can use a short and measure the amount of power reflected using a power meter or network analyzer or VNA. Now you connect the device you are testing and record the amount of power being reflected. The difference between the measurements is the return loss. The greater the return loss the better the match because less power is being reflected. A perfect match would not reflect any power. (due to limits in coupler directivity, noise floor of the power meter, or network analyzer probe, etc and other factors there will always be some apparent reflection.) Once you have the return loss you can calculate VSWR and refection coefficient.
Example: The measured reflected power with a short on the test port is -10dBm. When the short is removed and the device under test is connected the measured reflected power is -22 dBm. The return loss is the difference which is a return loss of 12dB, this is a VSWR of 1.7:1 and a refection coefficient of 0.25.
4a.) P1 dB Compression
This measurement is identical to 1 above except you keep repeating the measurement in 1 with an increasing power from the generator. At the point the gain measured is 1dB less than the gain with a smaller signal you are at the 1dB compression point. This is often referred to has P1dB or P1.
From the example in 1 the generator power was increased until the gain was 19dB instead of 20dB. The generator power was measured as +1dBm and the device Pout was +20dBm. The gain therefore is [Pout-Pin] = [+20dBm - +1dBm] = 19dB.
P1 can be specified at the input or output. P1input is +1dBm and P1output is +20dBm.
5.) Phase tracking
The phase through two or more devices is measured at frequency points across their frequency range and their transmission phase is record. The phase difference between the units at each frequency is the tracking. This measurement requires a VNA.
6.) Log linearity
At each frequency of interest measure the output voltage (Vlog) versus the input power (Pin in dBm) to the device from the generator. Plot the Pin versus Vlog and then calculate a bit fit line through the data. The amount of departure from this line is the amount of non-linearity. A quick method is to plot Pin and Vout on semi-log graph paper and place a straight line through those points that appear to be in a line. You will see the data curve away from the line at the low and high Pin values. A data point's distance from the line is the amount of non-linearity at that Pin value.
Note: There are a lot of subtle points not covered here, this is a broad overview, each measurement must be configured for the specific device and test set being used. If you have specific questions please post them.