Automatic targeting is most useful when you have sufficient firepower to destroy an enemy and do not want to be bothered with tactical combat details.  It relies entirely on your ships' battle computers to use just enough guns and missiles to destroy each enemy target before attacking the next one.  You simply identify the target empire and which of your ships are to be the attackers.  Your attackers will target the enemy ships according to the following criteria:
 

• Ships with the fewest remaining DP are targeted first.
• If two ships have exactly the same remaining DP, then the one with the smaller operational rating is targeted first.
• If two ships have exactly the same OR, the the one with the smaller tonnage is targeted first.
• If two ships have exactly the same tonnage, then they are targeted alphabetically by name or SN.
• Missiles are targeted after all non-missiles, and in the order of their tonnage (from smallest to largest).

 
Ships are targeted from smallest to largest in order to destroy as many individual ships as possible.  If you prefer to inflict damage on the heavier targets first, you can instruct your battle computers to target ships from largest to smallest instead. 
 
If a target ship is of an unknown foreign design, your battle computers will not know how many guns are needed to destroy that ship before the battle commences, and you will not know until the battle is over if you committed (or even possessed) enough guns to destroy it.