Recently, there was news that Hubble took a high definition picture of the Andromeda galaxy. I wanted to know how long does a high definition picture from Hubble takes to arrive on Earth; if at all possible, how does this process occur?
Hubble transmits about 120 GB of data per week (source: http://hubblesite.org/the_telescope/hubble_essentials/quick_facts.php). One picture of the original camera was only 640k pixels (this camera was built a long time ago), but the images you see are composited from many many images. Today, it uses WFC3 - a 8 mega pixel camera. Even so, a single image from the Hubble takes very little time to transmit - but depending on which composite image (dataset) you are talking about, the answer could be "a very long time".
The time for the radio signal to travel back to earth depends on the distance to the transmitter, but since its orbit is only 569 km above the earth's surface, it could be as little as 2 ms. From the furthest point it will be about 4000 km away, so it would take 13 ms for the signal to reach earth (speed of light ~300,000 km/s). Note that the article linked below says that Hubble doesn't in fact send data to Earth - instead it sends it to the geosynchronous tracking and data relay satellite system (TDRSS) twice a day, which will add some delays.
A more detailed answer is at http://en.wikipedia.org/wiki/Hubble_Space_Telescope#Transmission_to_Earth
And I just found this cool picture (source):
As for the size of the Andromeda data (the Panchromatic Hubble Andromeda Treasury), you can start at https://archive.stsci.edu/prepds/phat/ and dig down to the data files from there - for example, when you drill down to brick 1, you will come to https://archive.stsci.edu/pub/hlsp/phat/brick01/ and you'll see a long, long list of files that amounts to about 94 GB of data. And that's just for one brick. There are 23 bricks. But note that these are not raw image files as sent by Hubble. It seems reasonable to think it took a few months though.