As soon as you get the contact, look at the details, mainly speed and course. Use your map tools and draw a line along the enemy vessels reported course. So now you have a start point(where the report says he is) and a direction(where the report says he's heading). The trick now is to try and anticipate where he's going to be along that line at a time when you can intercept.
For example, my own personal rule of thumb;
If the report says the speed is "slow" I'll calculate the targets movement at a maximum of 5kts.
If the report says the speed is "medium" I'll calculate the target's movement at a maximum of 9kts(although I'll usually go with 7kts).
The idea being that if I over calculate his speed then at least I'll be ahead of the target as opposed to being behind and still chasing.
If the report says the speed is "fast" I'll usually not chase as that normally indicates a warship and I either can't catch 'em or I don't want to!!!
Using the nomograph I'll try and guess-timate how far the target can travel at the given speed along his route in a given time period. I'll also do the same for my sub on an intercept course but I'll check the distance first and figure out how fast I have to go to get there.
That's my crude method for at least getting me within either radar or sonar range at which point I can hopefully get the target on one of those and zero in.
Having said that, there's no guarantee your target will oblige you by staying on the course you think he's on. That's part of the challenge (and frustration, LOL).
Hope this helps. I'm sure one of the other more experienced boat drivers can give you a better method.