Turn the seacock off or you can simply turn off the valve located inside the livewell. The seacock is located in the bilge area (just lift up the bilge hatch and look for the lever valve) and the livewell valve is part of the water inflow spigot. Just remember if you leave the seacock on (open) and you have a hose failure the bilge will fill with water. I suggest leaving the seacock open only when you are actively using the livewell and/or raw water wash down.
What Inshore Chaser said... If you ever leave the boat in the water over night...Close it. This is a neglected item.....They do not get operated and thus are frozen when you would need to close it the most.
Another little story.....People that don't know anbout this will put valuable stuff in the livewell as a storage place and then find out they have ruined it when it gets flooded
How much water accumulates? You definitely need to check out where that water is coming from. With the seacock closed, there should be absolutely no water ingress. Does the livewell drain below the water line? Could it somehow be siphoning in through that?