A decibel is the RATIO of two quantities, usually power. 10dB is a gain of 10 times the power, -10db is a power reduction of 10 times.
Decibels are sometimes used as UNITS, hence:
dBm - decibels with respect to 1mW
dBv - decibels with respect to 1 volt
dBw - decibels with respect to 1 watt.
Where a meter is measuring voltage, but is calibrated in dB, it is important to know the impedance.
Usually for audio circuits, the impedance is 600 ohm.
So for a meter where 0.775v = 0dBm:
1mW = (0.775 x 0.775)/600 Try it, do the maths!
But for RF measurements the standard impedance is usually 50 ohm.
So here the meter will be calibrated so that 0dBm = 0.223v
1mW - (0.223 x 0.223)/50
As for finding the gain of an amplifier, measure the signal level at the input and the signal level at the output.
If we decide to measure voltage, and the input is 0.06 volts and the output is 3.6volts, the gain is 3.6/0.06 = 60.
If we measure in dB, and find the input is -13dB and the output is +17dB, the gain is +17 - (-13) = +20db
To find the gain (or loss) of a stage in dB, just subtract the input from the output.
JimB