From an end user's perspective one of the most important things to keep in mind is that the band configuration for Landsat 8 (LDCM) is different from the Landat TM and ETM+ missions as Landsat 8 added two new bands. Want to make a natural color composite from Landsat 8? It will now be R-G-B = 4-3-2 (for Landsat 4,5, and 7 it was 3-2-1). The USGS has a very helpful FAQ page listing the band numbers and wavelengths for all the Landsat missions. There is another handy USGS page that displays the band combinations of Landsat 8 to Landsat 7 (see graphic below)
Source: NASA
Landsat 8 will be 12-bit data, compared to the 8-bit data used for previous Landsat missions. Pixel values will now range from 0-4095 (4096 possible values) for Landsat 8, as compared to 0-255 (256 possible values) for the previous missions. This should make it easier to distinguish features that are spectrally similar and shadow penetration will be much improved.
Because Landsat 8 is not yet officially operational you cannot download scenes from sites like GloVis just yet, but you can download a sample dataset to play around with courtesy of the USGS.