How Earth communicates with Voyager I? After taking a basic signals & systems class and learning about the frequency domain, I started wondering:
How the heck do scientists still communicate with Voyagers I and II??
 
Do they send/receive signals in a frequency that is otherwise unusually silent? If not, then how do they send and receive faint signals from something 10 billion miles away, when the spacecraft has so little energy and where it seems practically impossible to aim everything 100% correctly (since things are so distant and moving at the same time)?
(I wasn't sure what to tag this, so please retag as appropriate, thanks!)
 A: As always, a communication via electromagnetic radiation depends on both ends. 
Uplink from earth can be done with a lot of power and big dishes, of course. 
Downlink is limited to the power of the nuclear battery on board but has a rather 
impressive 2.7 meters dish!.
On top of that they use a rather slow bitrate, I think with a lot of redundancy. 
All this is commonplace information technology when dealing with bad connections 
with signal not much above noise.
Details are given in Wikipedia: 

Uplink communications is via S band (16-bit/s command rate) while an X
  band transmitter provides downlink telemetry at 160 bit/s normally and
  1.4 kbit/s for playback of high-rate plasma wave data. All data is
  transmitted from and received at the spacecraft via the 3.7-meter
  high-gain antenna.

A: The question has already been answered pretty well, but I think more explanation of why big antennas help would be worthwhile ...
Antennas have a property called "gain" which means that they work best in one direction (or several directions, depending on the type of antenna) and less well in others -- so a transmitting antenna with high gain sends its signal in one precise beam, and a receiving antenna with high gain receives best from one precise direction and mostly ignores signals from other directions.
Well, the gain of an antenna depends on the type of antenna it is and the ratio of its size to the wavelength of the signal.  What this means for us is that if you want a really high gain antenna ... it has to be large compared to the wavelength of the signal.
The size of the antenna on the probe is fixed, but it's quite large, so it's got a high gain -- it sends its signal directly at where it knows the Earth is.  On the Earth, we keep using bigger and bigger antennas to talk to the probe, so we get higher and higher gains, and a high gain antenna aimed properly picks up more of the signal and less noise.
(There are other factors involved, of course, but this is why the big antennas matter.)
Note that the higher the gain of your antenna, the more important it is that it is precisely aimed.  But when we're talking to probes like this, we're aiming the antenna extremely precisely. 
But for something like the WiFi in your house ... high gain antennas tend to be a bad thing rather than a good thing, because it means that the range is good (better than a lower gain antenna) in the given direction(s) but bad (worse than a lower gain antenna) in others.
A: We know exactly where the spacecraft is, and it knows pretty well where we are. 
Distance does not aggravate the accuracy of aim problem, indeed the further apart the less relative motion, so aim gets easier.
The problem is signal attenuation by dispersal. i.e. at twice the distance, the signal will be a quarter of the strength.
The solution, for Voyager, has been that our earth-based recievers and transmitters have increased in both accuracy and sensitivity several times faster than the signal from Voyager has been weakening due to distance.
Indeed, if the power source would have lasted, we already have the ability to recieve a signal such a voyager's from thousands of times the distance.
The bigger your antenna, the tighter you can focus its view.
Once we get around to building the square-kilometer-array (2025 or so) we would have ability to hear a similar signal from several light years range.
