Finding Quicksilver Ore
There are many locations around skyrim were you can find quicksilver ore. However, there is one particular mine that is full of quicksilver ore veins. It is located in Dawnstar next to the northern most building on Dawnstar:
It is on the opposite side of the lake of the Dawnstar Museum at which you can find the Pieces of the Past Quest for which you can find a full guide here. If you have any trouble locating the mine I suggest you watch the video below which will show you the location in detail.
If somebody is blocking a quicksilver ore vein the best way to get at it is to kill that person. However if you want to avoid the hassle of being hidden etc you can wait for around an hour or so and the person will leave the ore vein.
Creating Quicksilver Ore
Quicksilver ore can be made from quicksilver ingots at a smelter. If you are at the quicksilver mine in Dawnstar you can find a smelter to the left of the entrance of the mine. Two quicksilver ore make a quicksilver ingot.