Matching preamp to amp

The simpliest way is to take preamp of the same brand as amp.

Other cases you should match the input sencitivity of amplifier to the gain of preamp:
If input sencitivity of amplifier is low than preamp should have a high gain or the other way arround...

Not all cases are trivial and you should also know the other variable such as input impedance. In trivial case the input impedance of amplifier should be 10x of output impedance of preamp but this ratio is valid if the output of preamp is relatively high since transfer of voltage has substantial losses and the losses are certainly not linear since you're dealing with complexed signal i.e. music.

The ideal case is when input amp's impedance is too high and the output impedance is too low but if the output voltage capabilities are substantially higher than input sencitivity of amplifier than even 10x-rule has its own tolerances in that case...

Kool39,
in cases with tube preamps you have enormous gain and output voltage to bring to the imput of amp. In this case you realy don't want the input impedance of the amplifier being too high since you will have much less volume controll capabilities from your preamp.
In case with passive preamp the philosophy stays near-same if you have high output voltage source. In my case I have passive/active pre with simple bipolar output stage that I switch sometimes when I play vinyl and turn off when I play CDs. I have approximately 0.5V out of my phono preamp with 0.5mV output cartridge and my VTL amplifiers have 0.55V input sencitivity(after recent mods). ON some records I feel lack of bass and have to switch the gain back-on and on some records it's plenty enough especially on 45rpms.