Power and Standby Switches

The mains power and standby switches are fairly straightforward, and can be found in almost every valve guitar amp. The mains power switch turns the whole amp on or off, and the standby switch turns the HT on or off. The general idea is to turn the power switch 'on' first, allow the amp to warm up for a few seconds, then turn the standby switch to 'on'.
Any switch with sufficient voltage and current rating can be used. Multi-pole switches allow other switching options, and rotary switches can be a useful space-saver. So called "progressive switches" are also available: these are multi position toggle switches. This allows an "off > standby > on" function in a single toggle. The same is possible with a rotary switch.

Mains power switch: The mains power switch is the main master switch for the amp. It is placed in series with the live wire (brown in the EU), before the power transformer primary winding. A double-pole switch can also be used to switch both live and neutral at the same time, or the second pole could be used to switch another part of the circuit such as an indicator light, although it is more common to use either a neon lamp across the mains supply or an indicator lamp run off the heater supply that requires no dedicated switch.
The mains switch will need to be rated for use with mains voltage and have sufficient current rating for the amp in question. Luckily most valve amps draw less than 1A from the mains (although this may not be true in the US/Canada where the mains voltage is lower).

Standby switch: The standby switch usually allows the HT to be turned off while the heater and bias supplies are always on. Contrary to popular belief, the standby switch is not there to prolong valve life-span. The theory is that if the HT is applied while the cathodes are cold they will be 'stripped' by ions crashing into the unprotected cathode. However, this simply does not happen. It is an urban myth borrowed from transmitter and cathode-ray tube technology NOT ordinary 'receiving' valves. The only valve which might ever be at risk of failure is a rectifier valve, because it has to supply inrush current to the reservoir capacitor, and some guitar amps fail to use enough limiting resistance to protect against this (see more on rectifies).
On the other hand, leaving a cathode hot without any anode current flowing does lead to the very real effect of cathode poisoning, which reduces the gain (transconductance) of valves. Fortunately this phenomenon really only becomes significant if the valves are left on standby for hours on end.
If you're wondering why all those old amps use a standby switch, its because they were designed on the cheap. The power supply caps would usually be rated only for the working voltage, not the peak voltage which occurs before that valves start drawing current. Leo Fender, and the rest, relied on the musician to use the standby switch to stop those caps bursting. The rest is history. Nowadays no designer (who values his reputation) uses underrated capacitors, so the standby switch has become obsolete, but your average amp tech doesn't know this.
Note that even the RCA Transmitting Tubes Technical Manual No. 4, p65, states: “Voltage should not be applied to the plates or anodes of vacuum, mercury-vapor, or inert-gas rectifier tubes (except receiving types) until the filaments or cathodes have reached normal operating temperature.” [My italics]. In a properly designed amp, a standby switch serves no useful purpose.

For those who still want a standby switch, perhaps because they've had bad experience with rectifiers... there are four common positions:
In series with the transformer centre tap or bridge rectifier ground connection. A switch in this position is commonly seen in old amp designs. Although it will turn the HT off, it does so only by breaking the ground connection, so the rectifier will still be at a high potential. Although it not strictly 'bad design' , breaking the main ground is frowned upon in modern designs.

Between transformer secondary and rectifier. With a two-phase rectifier this will require a double-pole switch. With a bridge rectifier a single or double-pole switch can be used, double being preferred as the most safe when working on a live amp as it completely isolates the transformer from the rest of the HT circuit. This method is most favourable because most high voltage switches are rated for AC mains use, so we can be more sure of their safe operation in the (slightly) lower voltage AC part of the circuit, rather than after the rectifier in the higher voltage DC part of the circuit.

Between rectifier and reservoir capacitor. The function of a switch in this position is quite straightforward and requires no explanation. However, in this position there is DC on the switch, which tends to cause internal arcing when the switch is thrown, shortening the life of the switch. This can be avoided by putting a diode after the switch (shown faint) so that only rectified AC appears across the switch, greatly reducing the chances or arcing. On the other hand, why not just move the switch to one of the positions discussed above?..

Where NOT to place a standby switch:
After the reservoir capacitor: This is not recommended as it tends to cause 'pop' sounds when throwing the switch. It and also puts DC on the switch too, which may shorten its life due to arcing.
Immediately in series with a smoothing choke: When the switch is thrown one end of the choke is left completely unconnected to anything. Consequently the choke will develop a massive fly-back voltage which could cause arcing in the choke or switch. This could be allayed by adding a protection diode in parallel with the choke (shown faint) but is still not a great design choice.

Improved standby switching:
Most standby switches simply turn the HT on and off, allowing the amp to be muted while the valves are still idling hot. When the standby is switched to "on" all the power supply capacitor will instantly draw inrush current;- this 'hard switch on' and inevitably shortens their working life. However, if we are willing to forgo the complete muting facility we can instead redesign the standby switch for a 'soft start' to truly help extend component life (especially the rectifier). If we arrange the switch to allow the anode current to increase very gradually at the same time as the heaters warm up, then both inrush surge and cathode poisoning can be completely avoided. This can be done simply by placing a resistor in parallel with the switch. Obviously this works best if the switch is placed before the reservoir capacitor.

Finding a suitable resistor is relatively simple because the amount of current we allow to flow on standby isn't that important, and it is in fact easier to decide instead how much power we want it to dissipate. Because the amp might be left on standby for some time we don't want the resistor to get very hot, and equally, we would like to avoid using a large and expensive metal clad resistor.
A 2W resistor would be ideal. To avoid excessive heat we will allow it to dissipate no more than 1W. At the moment the mains switch is turned on, the resistor will have to drop the full HT voltage. If the standby switch is to be placed after the rectifier we can use the value of HT voltage. If the switch is placed before the rectifier then use the AC (rms) voltage of the transformer.
In this example the switch is to be placed after the rectifier and the HT is 300Vdc. For 1W dissipation:
P = V^2 / R
(Note, ^2 means "squared".)
R = (V^2)/P
R = (300^2)/1
= 90 000 ohms
The nearest standard is 100k, but since it only has to suffer the maximum power dissipation at the moment of switch on, half this value or 47k would be fine too.
The initial current will mainly be swallowed by the reservoir capacitor so most of the HT will be dropped across our standby resistor, and the voltage on the valves' anodes will be negligible for the first few seconds while the heaters begin to warm. As the reservoir and smoothing capacitors charge the anode voltages will rise gradually and a small amount of anode current will be allowed to flow as the heaters reach full temperature. Once the capacitors are fully charged and the valves warmed up the amp will remain on standby, allowing a trickle current to flow at all times (so the amp will not be totally muted; there may be the faintest of strangled sounds if we tried to play). The current flowing will be small (and very difficult to calculate!) but sufficed to say that it will probably be about half the initial surge, and the anode voltages will all idle at somewhere in the region of half their normal value. The power now being dissipated in the standby resistor will be about:

This is an enormously simple modification to any amp, and any value over about 47k (2W) or 150k (1W) should do. A secondary advantage of this method is that because the filter capacitors are allowed to partially charge up during standby there will be little delay between switching the standby switch to "on" and sound coming out of the amp!

Heater standby switching:
The lifespan of a valve is considerably lengthened by running its heater under-voltage, at the expense of emission. Since we aren't using the amp when it's on standby, emission is irrelevant, so we could arrange for the standby switch to let the valves idle at a lower heater voltage. A standby switch on a heater supply is practically unheard of in guitar amps, but if you happen to have an unused pole on your regular standby switch then it could be put to good use. It is by no means essential, but a simple and beneficial modification.
Dropping the heater voltage down by about half could be achieved simply by switching in a suitably chosen resistor during standby. This is easy in a small amp with only a couple of valves but most amps have a heater current of several amps, meaning a very high power resistor would be in order. For example, a heater chain drawing only 2.5A would need a 0.82ohm resistor, which would dissipate nearly 5.2W!
A novel and cheap alternative is to switch a high-current rectifier diode in series with the AC heater supply. This will half-wave rectify the heater supply allowing the heaters to operate at half power (which is more or less the same as operating at half voltage), significantly extending their useable lifespan.