The reason why information can be transmitted in a useful way by electromagnetic waves is linearity of the electromagnetic wave equations, or in other words, the linear superposition principle. To put it simply, if you add together a signal (in the sense of an electromagnetic wave solution) in the frequency band 90.0-90.1 Mhz and another signal in the frequency band 100.0-100.1 Mhz, the result will again be a solution to the electromagnetic wave solution. Since this is true for all imaginable frequency combinations (including the composition of said frequency bands themselves), the frequencies do not influence each other. That is, by adding the signals together, there will not appear any new frequencies that are not part of the individual signals. Hence, information from the individual radio stations is conserved due to this linear superposition principle.
Water surface waves are a good example of a medium where the linear superposition principle does not hold. Hence, it would not be a good idea to transmit speech through water surface waves. If two people spoke at the same time, you would hardly understand anything behind all the intermodulation distortion.
Your example of colors is misleading, since the brain is "engineered" to compose multiple colors into one (and, therfore, fool you about the true nature of electromagnetism). If you use a prism, however, and decompose the colors into their spectral components, you see that nature is different behind the veil of sensory delusion.
As to the technical details of the extraction of a specific radio channel from the mixture of all channels, valid answers have already been given. Let me just add some more details. It would certainly be possible, to design something like a prism for radio waves, to sort out different frequencies at different angles. But this would involve several conductors in certain arrangements, and then it is much easier to use just one conductor (an "antenna") that pre-selects a certain frequency range by its resonant properties. However, the main purpose of the antenna is not to narrow-select a certain radio station (to the contrary, you would like to be able to receice a bunch of stations without swapping antennas all the time). The main job is done by the receiver (which is the "prism" for radio stations). The most important principle today for selecting channels is: Multiplication.
By multiplying a 100.05 Mhz sinusoidal signal to the 100.0-100.1 Mhz radio station, two distinct signals are generated (note that what happens in the receiver is therefore now a nonlinear operation! we are not in free air anymore!). The first one is the sum frequency, which will be a band at about 200 Mhz. This signal changes way too fast to be useful, and is thrown away (by applying a lowpass filter). The second signal is the difference frequency, which is in the band -0.05 MHz to +0.05 Mhz. Surprise, we need a lot slower circuits to decode this one. All the other radio stations will also result in sum and difference signals in the mixture, but the 90 MHz station for example will bereappear at about -10 MHz (difference) and +190 Mhz (sum), both being so fast, we can throw them away again.
Now that we have a signal that is around DC (-0.05 MHz to +0.05 Mhz) we can just filter out the other nasty high frequency stuff, and do some more post-processing, depending on whether we have an amplitude modulated (AM) radio station, or a frequency-modulated (FM) one. In any case we have isolated the frequency range where the information of interest is located. That is how modern software based radios (SDR) work, sometimes in the GHz range (mobiles, WiFi, etc.), where it is hard to find reliable electronic circuits operating that fast.
