Amplifier gain settings - what do they do?

Where are you seeing "gain settings" on a tube amp? They’re rare. Some old tube amps had input potentiometers whereby you could adjust "input sensitivity" on each input channel (Eico, McIntosh) - technically it’s not a "gain" adjustment, but an attenuator. These were quite useful (I enjoyed their utility) - the downside being that your signal is always going though a pot of (usually) not the best quality. I guess an amp could offer a few levels of (optional) input attenuation via discrete resistors. That’s actually not a bad idea - what with modern digital sources having such strong output levels, and tube preamps plus tube power amps usually having an excess of gain.

Other than input attentation, gain is dictated by circuit design, and in most tube amps there aren’t really any good opportunities / options to change the active cricuitry’s gain without also significantly affecting sound quality or performance parameters (e.g. variable feedback). There are very few stages in a tube amp as-is, and each has a prupose, so it doesn’t make sense to add an extra stage that could be switched in/out just for gain.

Solid state amps might have more options for this, and integrated amps could offer this in their preamp stage.

Turn the pre on first, then amp. Turn amp off first, then preamp. At almost 1500 posts here - you should know that by now? Anyways, most modern components shouldn’t give a THUMP on power on/off anyways (relay protections).

Adjustable gain levels have the following utility:

• Optimize system gain structure to lower noise floor (especially relevant for systems with tube pre, tube power, and high sensitivity speakers)
• Avoid overload conditions in any one component
• Place "typical" system volume control into a more agreeable range (various reasons)
• Fine-tune system left-right channel balance (if separate L/R controls)

Always turn your amp on last and off first. And I'd use the volume control on your preamp it's likely better quality then any gain pots or attenuators on an amp. Air Tight still makes amps with them and I'm sure a few other manufacturers do.

which amp and preamp? 

I always liked them, wish more amps had them.  Unless listening to music really loud it has been my experience that turning the gain down on the amp(s), which necessitates turning the preamp volume control up, will result in a slight but noticeable improvement in overall sound quality.  

I tend to believe most don't understand the distinction between gain, level adjustment, and volume control.  I have a pair of MC 901 McIntosh mono amplifiers and to read what it does is very confusing for my tiny brain.

I've always believe a true gain control increases voltage into the circuits to appoint where you can audibly here unpleasant distorted sound.  The level of intensity increases and finding the point just before this happens leads to the best quality in sound.

Amp on last so if a tube pops on startup or other large surge it will not go through the amplifier and damage the amp and or speakers. My Audio Research equipment is muted for 1.5 minutes on my preamp and 3.5 minutes on the amp... assuring the preamp is on and stable before the amp comes on. 

Gain... I've never owned and amp with a gain setting. 

I tend to believe most don’t understand the distinction between gain, level adjustment, and volume control. I have a pair of MC 901 McIntosh mono amplifiers and to read what it does is very confusing for my tiny brain.

I’ve always believe a true gain control increases voltage into the circuits to appoint where you can audibly here unpleasant distorted sound. The level of intensity increases and finding the point just before this happens leads to the best quality in sound.

It’s an interesting topic; wish I knew more about it. I’m certainly no electrical engineer.

From what I (try to) understand, many devices have limited ranges of optimal operation (loading and voltages) for lowest distortion - which is not conducive to coercing it into different gain levels. This is certainly true for tubes.

I guess you could look into op-amps (gain bandwidth product) or PS Audio’s so-called "gain cells" if you wanted to explore variable-gain circuitry.

In phono stages with active circuitry (not just a SUT with multiple taps), one "trick" is to have optional extra gain stages switched in & out to facilitate multiple gain levels. That’s not something you’d want to do in a tube amp.

As usual in engineering - the choice for greater flexibility usually comes with a cost: greater complexity, expense, and possibly sub-optimal sound quality parameters (noise floor, distortion, bandwidth).

IMO for a tube amp, a few discrete input attenuator positions (bypassable) is a good solution, and a better alternative than variable gain - it very cleanly addresses the *most common* problem, which is hearing the tube rush noise floor of a tube preamp when your system has too much net downstream gain. Each position could use very high quality resistors (Z-foils?) and you'd only need like 3 positions for good effect.