One of the easiest and most effective ways to get a breathtaking clean sound from your guitar rig is to add a different amp, or even two amps. The combination of different tonality and response adds a depth and complexity to your sound that goes beyond what you could achieve with any single amp. And it's easy to do, assuming that you have an extra amp or two. In most cases, you don't even need any extra gear aside from the amps and an extra cable or two.
If your amps have two inputs, typically labelled 1 and 2 or LOW and HIGH, all you have to do is to plug your guitar into one of those inputs and run a cord from the other input to the next amp. If you want to run three amps at once, simply continue the daisy-chain. It's that simple, really. The way the jacks are wired, your guitar's signal passes (almost) directly from one to the other.
There are exceptions. Some amps, typically channel-switching amps, don't have two input jacks. Too bad. And if you have an amp that sends each jack directly to a separate preamp section... Yup, too bad. At any rate, if your amp has two input jacks for a channel, try to daisy-chain it. If it's wired as 99% of guitar amps are wired, you'll be in business. If you have a low-powered Tweed Twin or one of a handful of even less popular amps, you'll find that the daisy chain doesn't work. No harm done.
Don't worry about loading your guitar down with the input circuits of two or three tube amps. The effects on the guitar's tone are minimal, easily compensated with the EQ on the amps, and more than overcome by the radical expansion in the complexity of the sound that you'll get by running multiple amps. If you want, you can spend two or three hundred dollars on specialty devices that fix this problem (and most of the others that I'll mention). Personally, I wouldn't bother.
Once in a while you'll encounter a problem or two. The most obvious problem is excessive hum caused by the daisy-chain connection. Your amps can be quiet on their own, yet hum when connected together. This hum is caused by a ground loop. What happens is that leakage current from the AC line to the chassis of the amp introduces a small voltage onto the chassis at the AC line frequency. This is perfectly normal; every amp does it to some extent. You don't normally notice it because the shield of your guitar cord and the guitar's wiring simply ride up and down with the small voltage fluctuations. There's no appreciable current flowing in the guitar cord, so there's no voltage loss from one end to the other; the ground voltage at your guitar is exactly the same as the ground voltage at the chassis of your amp at any moment in time. Since the amplifier only amplifies the difference voltage between the shield and the center conductor of your guitar cord, you don't hear any hum induced by the leakage current.
When you connect amps together, their leakage currents may be out of phase or of different magnitudes. In this case a measurable current does flow through the shield of the cable connecting the two amps, which causes a voltage difference between the shield and the center conductor. That difference is amplified and heard as hum. This is called "ground loop" hum. A small amount of hum is normal and, in most circumstances, perfectly acceptable. If you can hear the hum in a quiet room, don't worry. Play your guitar.
If the hum bothers you while you're playing at performance volumes, then you'll need to do something about it. First, be sure that your amps are plugged into the same circuit. The easiest way to do this is to plug them into the same power strip or extension cord. For those of you with older amps, those convenience outlets on the back may tempt you to daisy-chain the power just like you daisy-chain the signal. Usually, that doesn't work out well. Invest a few bucks in a power strip - the cheap ones are just as good as the expensive ones for this purpose. Some older amps have ground-reversal switches; try these (in all combinations if more than one of your amps has a grounding switch) in all combinations.
The pros will resort to using ground cheaters if needed. A ground cheater disconnnects your amp's safety ground to eliminate one path for the ground current; sometimes this will help. But when you do that you're relying on a signal cable between the amps to carry a fault current and pop the circuit breaker if something bad happens that dumps full line voltage onto the chassis. It doesn't happen often, but it does happen. And finding out about it the hard way can be painful, debilitating or fatal.
By the way, if you have an amp that doesn't have a three-wire AC line cord and grounding plug, don't use it. Take it to a tech and get a proper three-wire cord installed. This applies whether or not you're running that amp in a multi-amp setup.
If you're going to play with ground cheaters (and I strongly recommend that you never use them) there are a few precautions that you should take to minimize your chance of accidental death:
- Never use a cheater on the amp into which you plug your guitar cable.
- Plug all of your amps into a power strip, and plug the power strip into a portable GFCI (Ground Fault Circuit Interrupter). You can get these for around $20, which is not much to save you from possible death by electrocution.
- Check the stage or rehearsal-room power with one of those three-light outlet testers before you plug in your power strip. Think of the tester as a five-dollar investment to let you keep playing your guitar, unhampered by an untimely demise.
- Make sure that the power is turned off at the power strip before you add or remove the daisy-chain signal cables.
- Turn all of your amps on (both power and standby) before applying power at the power strip. When you're done playing, turn off the power at the power strip first, before turning off the amps' power switches.
- Don't hold your guitar's strings (or other metal parts) and touch any amp at the same time.
Does that sound like a lot of trouble? If it does, then don't use ground cheaters. EIther that, or get your Last Will and Testament in order... You'll probably get away with breaking all of the above rules. But do you really want to gamble with your life? Musicians do die of electrocution.
Still with me? Good. Ground cheaters are bad. Don't forget it.
In 2004, Ebtech introduced a product called the Hum-X Hum Eliminator. This breaks ground loops just like a ground cheater, but still provides a safe path (i.e.: not through your heart) for ground fault currents. They sell for about $60, and they're safer than using a ground cheater.
OK, now that we've established that intentionally defeating safety grounds is dangerous, let's look at the rest of the things that can mess up a multi-amp setup.
You might notice a loss of bass response in your multi-amp setup. This is a result of phase cancellation. If you have amps with reverb and dry channels, try running the daisy-chain connection through the other channel. In many amplifier designs, the reverb and dry channels have opposite phase relationships. If your can't do that, or if it doesn't work, try reversing the speaker wires to reverse the phase.
Finally, keep in mind that little things can and do go wrong. I had a strange sound in my two-amp setup that sounded exactly like a microphonic preamp tube. Swapping tubes didn't help. It turned out that the connector shell had loosened and was rattling on one of the plugs on the cable that I was using to daisy-chain the amps. Because of its proximity to a sensitive signal path, the intermittent ground to the loose shell was causing an electrical disturbance that got amplified. Strange, but true.
 Yes, the standby switch. If you really believe that powering up your amp without the standby reduces the life of your tubes, then just factor in more frequent tube replacement as one of the costs of electrical safety while using ground cheaters. A very few extremely high-powered tube amps have plate voltages high enough to make a standby switch a true necessity for prolonging tube life; you're not likely to find any of these amps in a multi-amp setup.