So, something of Comet ISON has clearly survived its encounter with the Sun, but astronomers are still unsure exactly what made it -- a bit of the nucleus or a cloud of debris. This is where Hubble will come in. Once it's safely away from the Sun (Hubble cannot observe objects too close to the Sun, for fear of damaging its delicate optics) and in a good position to be viewed, around mid-December, Hubble will observe ISON to see if there's anything left of the nucleus.
At this point, it's doubtful that ISON will be visible to the naked eye in the night sky. There just doesn't seem to be enough left of the comet after its pass by the Sun. ISON has surprised everyone before, though. If ISON were to become visible to the unaided eye, it would be around Dec. 6-7, according to the observers at NASA's Comet ISON Observing Campaign, whose blog has great, in-depth analysis of the latest news.
Here's the lastest from NASA's Solar and Heliospheric Observatory, which has imagery through Dec. 1. Notice how whatever's left of ISON appears to be fading away at the conclusion.
And here's the latest ...