Improving the dredge uses carpentry tools and logs, but improves blacksmithing skill.
To use a dredge, while in a boat such as a Small Rowing boat, you simply float on top of the tile you want to dredge, and right click the tiles below and select "Dredge". Dredging will also make the tile you dredged steeper, just like normal digging. There is no specific boat to dredge from. There is no such boat as a "Dredger".