How do I find where the cursor's position is in the world?

You need raycasting. Here's the function I use:

function Convert2DTo3D(camera, x, y, maxDist, ignoreList)
		--returns the object hit followed by the coordinate hit
		--maxDist and ignoreList are optional. ignoreList can be a table or an instance.
	local ray = camera:ScreenPointToRay(x, y)
	ray = Ray.new(ray.Origin, ray.Direction * (maxDist or 999.5))
	local basePart, hit
	if type(ignoreList) == "table" then
		basePart, hit = workspace:FindPartOnRayWithIgnoreList(ray, ignoreList)
	else
		basePart, hit = workspace:FindPartOnRay(ray, ignoreList)
	end
	return basePart, hit
end
--Sample usage:
print(Convert2DTo3D(workspace.CurrentCamera, 50, 100))

In the example case I used coordinates 50, 100. You'll want to use the mouse's actual coordinates; possibly on MouseMove (see UserInputService)

The general idea is really just these two steps:

• Convert where the mouse cursor is into a ray using ScreenPointToRay
• Raycast this ray to find what it hits using one of the workspace's functions