It's actually fairly simple.
Start by shooting a 360 degree panorama [you can do it on 180s etc just as long as each end of the panaroma looks similar], try to ensure your shots overlap by around 20-30%. I did these hand held but you'll get better results on a tripod and better still if you have a panoramic head.
Next, stitch them together to create a flat panorama and crop. I used Hugin to do this [freeware] which I prefer, but Canon's Photostitch or Photomerge within Photoshop/Elements should do the job I'd guess.
So far so good, here's where the "weird" stuff starts!
You need to resize your panorama to a square, so click Image>Resize and ensure that Constrain Proportions is unticked. Select the same figure in both height and width boxes [the power of your computer will dictate how big you can make it, I went for 4000 pixels].
Next, rotate the shot by 180 degrees and apply the Polar Coordinates filter found under Filter>Distort.
There's your basic "planet", all that's left is cropping or painting in areas you want removing/filling plus some healing brush work to tidy it up. I then sharpen slightly on a duplicate layer but apply a circular gradient on a layer mask to avoid sharpening the centre as it all gets a bit strange there.
And that's it, simple eh!