[Bill Walker]

The Mark I eyeball, and a compass to start.

Bearing can be found from the ship's wake, referenced to your magnetic compass.

If you have a rough estimate of ship size, which is based on type, which is based on your studying of Jane's All the World Navies before you go (both sides used it), you can get a rough estimate of speed from the contained angle of the visible wake.

Back on ship, successive plotted locations and observed times would be plotted on a map, then a more accurate measure of heading and speed could be found after a second or third reporting. This works best if heading and speed are constant of course, hence zig-zagging. The greater the difference between visual reports of speed and heading, and the long term calculated speed and heading on a map, the more the target is zig-zagging. This can tell you if your target expects to be attacked soon.

Precision of all this was not great, but good enough. You didn't use position reports to aim weapons back then. You used precision reports to allow the next flight, or a ship, or a sub, to get close enough to visually locate the target in a short period of time.