Different frequencies working together How do the different waves of EM spectrum present in the environment not interfere with each other? If they do, how does everything work properly?
The radio waves of mobile phones and wi-fi work together. Why don't they collide with each other, since they are physically present?
 A: They do interfere with each other, but the outcome is not a problem so long as the device that's receiving or using the signals is tuned to pick out the relevant frequency.
For instance, resonant circuits will only be driven properly in a narrow range of frequencies around the resonant frequency. A mixture of waves with different frequencies will effectively be filtered by such a circuit to pick out the signal of interest.
Where you do get problems is broadband interference or noise that covers a wide range of frequencies, because obviously some of this will occur over the narrow range of frequencies that a device uses.
A: Actually, the physics aspect of this (linear medium => superposition principle => waves of different frequencies don't interact) is just a small part of what makes interference less of an issue.
All modern commercial wireless communication systems (like Wifi and cellphones) assume interference is present, partly simply because the frequency spectrum for regulated commercial transmissions is very tight to begin with (and so the probability of collision/interference is actually high) and partly because as the segment of time you communicate over becomes shorter and shorter, the frequency bandwidth over where you're sensitive to interference becomes wider and wider.
It is handled at a low level by the same methods as in resilient military transmissions - you don't put all your eggs in the same frequency basket, but use various spread-spectrum techniques.
In the military case you're concerned about intentional jammers, in the commercial case you're concerned about both that an unintentional jammers like your microwave and the sheer density of devices and wireless networks occupying roughly the same small frequency spectrum.
One very simple to understand technique is frequency hopping, where you continuously hop between different frequencies over a wide band (or, as wide as the regulatory agency allows you to) and if one hop has interference, you can detect this and resend the information during another hop.
A conceptually a bit more complicated technique is to actually use the issue I mentioned above (small times => larger bandwidth of interference) but in reverse - if you add a lot of redundancy to your signal and send it much faster, the bandwidth of the signal increases and by the same reason that frequency hopping is resilient to narrow frequency jammers, the now redundant signal still gets through.
You can read about this on wikipedia.
As an (simplified) example, suppose you want to send the short signal sequence 101 to someone, and you would normally send this at 1 MHz (1 million "letters" per second) modulated over a frequency wave of 1 GHz. Your resulting transmission would be centered around 2.4 GHz and 1 MHz wide.
So, a 1 MHz wide jammer at 2.4 GHz (like your microwave oven) would kill everything in your transmission.
Now instead lets increase the signal rate by a factor of 10, by randomly assigning sequences of 10 digits for each 0 or 1 digit you want to send, so for example 0 => 0100101010 and 1 => 1110101110. 
This widens the bandwidth by a factor of 10, as the resulting signal rate now is 10 MHz and your transmission will still be centered around 2.4 GHz but now at 10 MHz width.
Your 1 MHz jammer will just "hit" 1/10th of your total bandwidth, and since there is a large redundancy of your signal, you can still recover it perfectly even if there are some loss of digits.
For non-toy protocols, the spread is much higher than a factor of 10, and the resilience can be very high. For example, the GPS protocol sends a signal from a satellite orbiting 12000 miles high (21000 km) at a power level of a few hundred watts. When you receive the signal down on the ground, it is buried in noise, about 26 dB beneath the noise floor! The receiver can still demodulate this due to the spread-spectrum technique used for spreading the signal.
Another way to see all this is that with a constant power level budget in your transmission, you can either send a narrow bandwidth strong signal, or you can send a wide signal with a lower maximum strength, which might be under the noise floor of the receiver. But the receiver can "push" the wide signal back together into a narrow shape, and then it will rise above the noise floor again, allowing you to recover the data.
So to conclude, the reality of commercial transmissions is that the spectrum is tight, there are a huge number of unintentional jammers and interferers and this is taken care of at the RF processing level and upwards (communication protocols that use Wifi for example also have error checking and resending etc. built in).
A: It's a good question, but the answer isn't particularly simple.  The wikipedia page on the Superposition Principle is a decent starting point.  If you feel like you understand the basics, there's a nice simulation of superimposing different frequency components that might illustrate the idea for you.
