Wipe the silicone off quickly with a paper towel as soon as it hits the sink pipe. If it's still wet, you can get most of it off simply by wiping it.
Scrape the majority of dry silicone off a pipe, using a rubber or metal spatula.
Use the edge of a razor blade to remove silicone from jointed areas or to scrape off thin layers. Once some of the silicone sealant is loose, you can usually pull much of it off in strings.
Scrub the area with a mild detergent and some water applied to a scrub pad. Dry the area thoroughly before continuing to apply sealant.