In the top image I used a high frame rate camera recording at 23 frames per second for 3000 frames, I then used software to select the best 300 frames and combine them to allow me to produce a relatively sharp image that clearly shows the rings as distinct from the planet. You can also see the Cassini division which separates the darker 'A' ring on the outside of the disk from the brighter and wider 'B' ring. Above the disk of the planet you can make out Saturn's shadow being cast over the rings and conversely where the rings cross the planet you can make out hints of the shadow of the rings cast on to the cloud tops of Saturns atmosphere.
But of course Galileo didn't have a high frame rate camera, or a computer capable of sorting and stacking the frames, he also had no prior knowledge of what he was looking at!
The lower image is the same as the upper one but blurred to simulate the relatively poor optics and the effect of the atmospheric "seeing" that Galileo might have experienced at the eyepiece.
The video clip below is an unprocessed export of part of the video I recorded through my telescope, keep in mind that this video clip is much sharper than the view through Galileo's telescope would have been due to the size of my telescope compared to his. Its not hard to see why he was a bit confused!