Everything you need to know about Manual Targeting and then some:
http://www.paulwasserman.net/SHIII/
Basically the 3:15 rule means you mark the position of a contact/ship on the map then start the chronometer (From the attack scope/UZO screen). After 3 minutes and 15 seconds you mark it's new position. Use the ruler to measure how far apart the two marks are. That range divided by 100 = speed in knots. So if it moved 600m in 3 minutes 15 seconds it's speed is 6kts. If it moved 1.2km in 3:15 it's moving at 12kts.