I've read that some people make their marks on the contact line that extends from their sub at the point at which the line starts fading away. Inexact but it's a start.
I use a slightly different method:
Assuming the ship is reported as being at a "constant distance", I pick an arbitrary measurement with the ruler, say 6km for one that's reported long distance. I will make a couple of markings along the contact line at "6" from my sub, and at different intervals which will give me either the contact's course, or one that is parallel to it. By then using the nomograph on my map (download the mod) I have the distance travelled by the ship between two markings, as well as the time it has taken it to travel this distance, I therefore get a very rough estimate of the ship's speed.
Having his speed and rough course, i can plot a course that will give me a general intercept course.
Frequent hydrophone readings when i reach that spot will allow me to fine-tune my position.
Does any of what I've written make sense?