So I have briefly gone over answers to how things are stored as from this answer: https://space.stackexchange.com/a/2273/1247 but how is the information sent back? I'm thinking of probes like the Voyagers, the Pioneers, the Mars probes and Hubble.
Mostly it's by radio waves.
Some "information" is physically transported back to Earth. The Apollo missions brought 382 kg of lunar samples back to Earth and the Soviet Union Luna program brought 0.326 kg of lunar samples back to Earth. That kind of return is highly valuable information. Even with the success of the Mars rover programs, a Mars sample return mission would still provide very useful insight into the geology of Mars.
Recently NASA has experimented with using lasers instead of radio communications. The much higher frequencies associated with laser communication have the potential of a much higher communications rate. The Lunar Laser Communication Demonstration on the Lunar Atmosphere and Dust Environment Explorer achieved a 622 megabits per second downlink rate. That's orders of magnitude higher than the rate achievable with radio waves.
Update regarding latencies:
The speed of light dictates the latency for vehicles well beyond the Earth such as the rovers at Mars and the New Horizons vehicle en route to Pluto. The one-way travel time between New Horizons and Earth will be around 4.5 hours when the vehicle flies by Pluto. Commands need to be sent at least 4.5 hours in advance, making for a 9 hour delay between sending a command and receiving the vehicle's response to the command.
For vehicles in low Earth orbit such as the ISS and the Hubble, speed of light is but a small part of the communications delay. Watch a NASA video where mission controllers talk with the astronauts aboard the ISS. There's about a good four or five second delay, even for simple questions such as "ISS crew, are you go?" The one way travel time between low Earth orbit (or Earth surface) and geosynchronous orbit is about a quarter of a second. Double that and you get half a second for round trip light delay.
So where does that extra four seconds or so come from? The answer is bits bouncing around inside and between computers. The mission controller's "are you go?" query is digitized, mixed with other signals to be sent to the ISS, and transmitted via ground links to White Sands. The signal enters White Sands at the NASA Ground Terminal, where it is mixed with other signals that will eventually be sent to the appropriate Tracking and Data Relay Satellite. The signal constructed by the NGT next makes a short hop to the White Sands Ground Terminal, which does even more data manipulation. The signal is next send to an antenna and transmitted to the TDRS. The signal arriving at the TDRS has to be split into component parts, another computer at work. That signal is sent to the ISS, where it goes through yet another computer before the crew hear it. The entire process is reversed when the crew reply "Go!" to the query.
As David said, probes generally communicate via radio. Long-range space probes often carry a dish antenna.
A parabolic dish antenna focuses the signal into a narrow cone. Compared to a standard wire antenna that transmits evenly in all directions, a dish makes sure as much of the signal as possible is sent in the direction of the receiver.
This gives the strongest radio signal possible within the limited power budget of the probe.
For space probes that aren't in Earth orbit, NASA operates the Deep Space Network (DSN): a series of large dish antennas designed to receive the very weak radio signals from far-away space probes. They can still communicate with the Voyager probes on the other end of the solar system.
For Mars ground missions, the rover or ground station often communicates with an orbiter. The orbiter relays the signal to Earth.
When you use a dish antenna on Earth, you can make it very large, in order to gather more of the signal. The larger the dish, the weaker the signals it can pick up.
As the last step, the receiver on Earth is very sensitive. The receiver is often cooled to very low temperatures to reduce noise.
As a result, this chain (transmitter with dish antenna, sensitive receiver with large dish antenna) can pick up a 10 W transmitter from 100 AU away.
Hubble is close enough that it doesn't need the DSN. It's in low Earth orbit, so latency isn't really an issue. For Mars, latency is on the order of 15 minutes. For Voyager, it's around 15 hours (one way).