Once you've mastered the basics of combat and can design effective ships, it is time to delve into some more sophisticated space combat tactics. The AI is rather predictable and usually employs very little variation in its tactics. This guide attempts to only cover single player with ship initiative enabled. It goes without saying human opponents can be much more unpredictable, and need other strategies when being played against.
Once the combat screen opens, assuming your fleet didn't get blasted away before having the chance to react, it is time to decide whether to fight the battle or to retreat. If the enemy has a Warp Dissipator, you might be forced to accept defeat but fight to inflict maximum damage on their fleet. It is recommended to turn on the following options: missile warnings, show legal moves, and show shield arcs (if you have them). This way you won't accidentally charge into a missile salvo, and can determine movement more effectively.
Hit the scan button and do a detailed analysis of the ships. The AI ship design is rather predictable, but in any case look for any beam weapons with high damage potential or (most importantly) EMG-equipped missiles. See also if they have good leaders on their ships, and try to take out those ships quickly. Battlestations and Star Fortresses add bonuses for any defending fleet, so those should be the primary target.
Attacking and maneuvering
Once you've identified the most dangerous ships or planet defenses, it is time concentrate all your firepower on those target(s) until they are destroyed. Try not divide your firepower too much, or otherwise the enemy ships will have more time to keep shooting at you.
If the enemy has a lot of ships clustered together, it might make sense to shoot the ones in the middle first, so any engine explosions would damage nearby ships. Once you have the Achilles Targeting Unit, this becomes even more effective.
If the AI fleet launches missiles against you, usually they all target the same ship. Try to determine it by their direction, or by moving a ship one square forward. If the missiles also move, they are targeting the ship that moved. If the ship's Point defense beams can handle the salvo, go ahead and charge forward until you get the missile warning. Then shoot at the missiles point blank with Pd.
On the other hand, if there are more missiles than you can handle, try to move your ship away from the missiles. If you can finish the turn without missiles hitting the ship, usually your other ships will have a chance to shoot at the salvo before it hits the target. Missiles will always travel to their primary target even if other enemy ships travel right past them, so take advantage of this. Later on in the game with good Pd, you can expect to shoot down 100% missiles before they even hit their target.
On the other hand, torpedoes can't be shot down at all with Pd, so your only counter-measures are using an ECM jammer or some special systems, such as the Lightning Field.
Using shields effectively
If you have Class III shields or better, they too can be used for maximum effectiveness with some maneuvering. Shields are divided into four arcs which all operate individually. So it makes sense to rotate your ship so that the AI is always shooting at your undamaged shield arc. When the other arc has regenerated, you can rotate the ship again. Better yet, rotate the ship so that enemies are shooting at multiple shield arcs. This way you can at least double the effective strength of shields. Paired with Hard Shields or Multi-Phased Shields, you can win many battles with zero damage. If you plan on using this tactic, make sure you set your weapon firing arcs to forward ext. or 360 during the design phase so you can continue to return fire while facing sideways or backwards.
Attacking using missiles
Missiles work best when upgraded to ECCM/MIRV/Armor/Fast, fired from massed fleets, and using Fast Missile Racks. Emission Guided missiles should be placed in the lower rows, so they aren't shot down first by enemy Pd. A common tactic is to use one unarmed scout, which runs to the map corner, while the missile ships retreat immediately after firing all their salvo (can be considered exploit-ish against the AI). Scan your enemy, take out support such as Star Bases (which give fleet bonuses), leader ships, planetary weapons first.
Often the most difficult part in attacking using missiles is to estimate the necessary amount to adequately destroy the target. If you use too many missiles, ship drive explosion can wipe out all missiles nearby needlessly, and shooting all the MIRVed merculites at a planet can net thousands of points of damage which kill everyone inhabiting it several times over.
Winning defensive battles
You need to be aware that you may not be considered the defender even if you control the star system in which the combat takes place. If you elect to attack the enemy fleet, you are considered the aggressor, regardless of other considerations. This means that you cannot use your planetary defenses in such circumstances. Keep in mind, though, that if neither side engages combat, your planets in the system will be blockaded.
Once you are in combat, you should decide whether it is advantageous to wait. If your opponent uses missiles, waiting can help you shoot them down (if you go first, they won't have fired any missiles yet). Even if they're using beam weapons, you can close the distance between your ship and theirs more easily if you go second. Of course, waiting does you no good if the enemy is capable of destroying your ship before you get a chance to react! The reverse is also true: waiting probably does more harm than good if you can destroy their ship before they have a chance to react, as well.
Winning in ground combat
Ground combat is much simpler and there is not a lot of options. The two factors that determine the winner are the Ground Combat rating and the number of troops. For each 10-20 point difference in combat rating, the weaker side will need double the troops to win the battle.