How do radio waves reach receivers without being canceled out by interference? 
When I think of waves traveling through a medium, I tend to think of the double slit experiment or waves in a pond. In those cases, waves are canceled out by destructive or constructive interference.
I'm curious as to how the EM wave can be sent out through an antenna without being canceled out by other EM waves from nearby antennas (or attenuated when it travels through some attenuating medium)? How is it possible that I am able to hear the sounds from the radio knowing that it was transmitted by a radio tower miles and miles away?
Or rather, if the magnitude of the EM wave is not of concern, then what exactly is the information which is sent and what information is received and decoded by the receiving antenna?
 A: So, in the case of waves traveling through a pond, if you imagine the transmitter as the rock hitting the pond and the receiver as, say, a frog sitting in the water, then you can see that the frog feels the waves that bounce back or interfere with each other, but the first wave that hits him will be the strongest.
While a wave is traveling, a significant amount is attenuated/lost, and only a small amount (10^-6 or less) of the original signal makes it through to the receiver.  The receiver then filters the signal received from the antenna to only "look at" a particular wavelength of the RF spectrum and then demodulates it.
The exact details of the signal sent by the transmitter depend on the transmission mode.  There are many kinds or modes of transmission.  Some common modes are FM (Frequency Modulation, AM (Amplitude Modulation), SSB (Single Side Band) for transmitting voice, or one of the many modes for data transmission.
If you are talking about the kind of radio that they play music over for you to listen to in your car, then you are most likely talking about FM.  Frequency Modulation (FM) works by changing the frequency of the radio wave that is sent.  If you tuned your radio to 95.5 MHz, then what you are receiving is a radio wave that has an unmodulated frequency of 95.5 MHz.  What the transmitter does is take this 95.5 MHz signal, and modulate it (i.e. they change the frequency slightly to transmit voices or music).  Then, at the receiving end, your radio takes this modulated signal and extracts the sound from it.
A: Good question.
If you look at a list of radio stations in the UK you will see that most of them (and all of them that cover the whole country) use several different frequencies to broadcast precisely because of this problem. (look at the AM list which is clearest on this point - AM = amplitude modulation).
Radio stations that cover a large area use several frequencies so that in places between transmitters they do not have the interference problems that you talk about in your question. So neighbouring transmitters broadcast on different frequencies.
The electronics in radios can pick up individual frequencies very nicely so that you only here the station you are tuned into, but if two stations were broadcasting on the same frequency there would be real problems because of intereference.
So to answer your question inteference is a concern and stations that broadcast from several antennae use different frequencies.  
A: 
Or rather, if the magnitude of the EM wave is not of concern, then
  what exactly is the information which is sent and what information is
  received and decoded by the receiving antenna?

Let me give you some perspective on this, as it's a point that is often overlooked.
The whole reason you can receive a (weak, as you say) signal in the distance, is due to the massive redundancy of using an oscillating EM field, as opposed to, say, a single EM spike.
To give the idea in a super-simplified form, imagine a 1 MHz transmission as hammering on a telegraph key (EM "clicks") 1 million times a second, and then your buddy is listening to this and keeps the rythm with his left foot (he is very fast!). He knows the speed the beats should be coming with, and just tries to find the corresponding rythm.
Even if the signal is very weak and he misses say 80% of the beats, he can fill in the rest since he is keeping the rythm and knows where to listen.
So by deciding beforehand what rythm you and your buddy should communicate using, you can counteract the lossy medium and send a resilient signal (you could encode the message by slightly perturbing individual groups of beats backwards or forwards in time for example, this would correspond to FM radio then).
If someone else transmits on another frequency it doesn't affect your transmission as it would just drown in the rest of the noise the receiver hears.
Fortunately, you don't need to click on the telegraph key millions of times a second and find a buddy with a fast ear. In amazing convenience, nature provided us with the electrons, photons and metals. Depending on the actual frequency, you and your buddy are electrons spinning around atoms or flowing through a conductor, and the beats' best analogues are virtual photons, building up the transmitted photon.
This turned out a bit long-winded, but it's such a basic feature of physics and information that is often not appreciated.
A: What makes you think they don't?
When I was a wee lad, my physics teacher showed a video to me of exactly that. A man was driving down a road listening to a radio station (BBC if memory serves). At regular intervals, the music would get quieter and cut out.
The issue was that the road in question was nearly along the line between two radio transmitters, which setup a standing wave between them.
This is typically a rare occurrence, as governments have setup agencies to govern usage of radio frequencies, in hopes that this wouldn't happen.
