What kind of spider web is this - and how do I get rid of it?
Here's what I found from the Univ of Kentucky';s Ag school site: http://www.uky.edu/Ag/CritterFiles/casefile/spiders/funnel/funnel.htm


  Funnel weavers and grass spiders build funnel-shaped webs close to the ground.  The spider hides in the narrow end of this funnel, which is usually protected by leaves or rocks.  When an insect, spider, or other small creature crosses the wide end of the funnel, the spider feels the vibration and rushes out to grab the prey.  Funnel weaver and grass spiders are incredibly quick, and can dash from the protected part of their web to the other end at lightning speed.  These spiders are common in many Kentucky habitats, including lawns and on the forest floor.
  
  Funnel weaver and grass spiders are beneficial predators.  They very rarely leave their webs, so they don't often enter homes.  They will only bite if provoked, and are not considered dangerous.
  
  Grass Spiders are very common in Kentucky.  We have several species, but they are all virtually identical in appearance and behavior.


 

Seems to fit your description.