You get preamp valve distortion by simply running them hot. So basically... with one dual triode standard valve like a 12AX7, one triode into the other produces very little distortion. Hence why early amps had few gain stages.
Cascading gain amps use a multitude of 12AX7s, each with two gain stages. So amps like a JCM800 which have I believe 4 gain stages already become way more overdriven in the preamp stage.
To overdrive your power valves, you need to send them a strong signal. So in older, high headroom Fender amps, you had to run the volume all the way up. The 'volume' control is what we would now call gain, our 'volume' being placed usually a little after along the signal path.
So you'd get your clean sound louder and louder, introducing only negligible preamp distortion. After a while your power valves will distort.
Power valve distortion is less thick and more harmonically rich. It preserves note clarity. Think AC/DC. Against say, Metallica ;)
In THEORY it works with transistor amps as well.
For more modern amps... The power stage is usually designed to be pretty neutral and offer as high headroom as possible. So it's harder to overdrive the power valves. And obviously you need your amp WAY louder. But it does brings out a little more gain. But those amps are built so that the distortion comes from the preamp.
Hope this helps :)