First of all, keep in mind that at all times your crew knows your sub's own speed and true course.
When you send the range/bearing of a target to the fire control crew, the bearing is relative to the bow of your sub. Given the relative bearing, as well as knowing your sub's course, gives you the true bearing to the contact. For example, if the relative bearing is 350 degrees (10 degrees to the left of your bow), and your sub is heading 45 degrees from true north, the true bearing to the contact is 35 degrees.
To get a visual representation of your target's location, get a range/bearing value. Convert relative bearing to true bearing. Draw a line from the position of your sub on the map. The length of the line is the range you measured, the direction of the line is true bearing. Mark an X at that spot.
Do that twice and you have 2 marks. Connect the two marks with a line and you have the target's course. The target's speed is the length of that line divided by the time between the two measurements.
Getting true bearing is easy; you know your sub's course exactly, and you know exactly where your periscope is pointing when you send relative bearing to your target.
Getting range is a less exact. Whether you use the stadimeter, sonar pings, or radar, there is some error in the range measurement. However, if you make many range/bearing measurements, the errors will tend to average out and you will get a reasonable estimate of course and speed.
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