If the airport has a Cat III ILS approach and if the crew and aircraft are certified for Cat III, then they can land in almost zero visibility. However, many commercial airlines have company operational procedures that prevent landing if the RVR (runway visual range) is less than a certain value and this varies among different airlines. Usually it is in the range of 1600-1800 feet. If they can't land then they hold at a specified waypoint or intersection or they divert to an alternate airport.
Only major airports have Cat II and III ILS approaches so if you are not at one of these then you have to hold till the weather breaks or divert to an alternate.
During low IMC the controllers constantly give out the RVR at touchdown, midpoint and rollout along with the ceiling so the crew is made aware of landing conditions well before the approach is attempted.
Check the Bad Weather listings on LiveATC homepage and you may be able to hear some low IMC approaches and diversions.