How can I create a "master" switch with sub-switches all connected to the master switch? When then master switch is turned on, it allows power to go to all the sub-switch (when the sub-switches are on). When a sub-switch is turned off, its output cannot receive power.
It sounds like you want a lot of AND gates (sub-switches) with one common input (the master switch) in each gate.
Note: The piston is just an example of an output device.
Try constructing one AND gate for each sub-switch and connecting all the "A" inputs to a single lever and each "B" input to its own lever.
When connected properly, each AND gate will not be able to output power unless both the master switch is on and its corresponding sub-switch is on.
Be aware that redstone signals will only travel 15 blocks. A repeater can be used to extend this.
Take a look at redstone AND gates. The Minecraft wiki article has some great examples (in the image below) and searching YouTube will turn up a bunch of great tutorials if you need more help.
Basically, every output is an AND gate with one input being its own switch, and the other input being your 'master' switch. If your master switch is off, all of the AND gates are also off. But if your master switch is on, then the AND gates are either on or off depending on the state of its subswitch.