Oddly enough this UI appears to be missing from the manual.

Note: I might be a bit wrong on the damage formula. How damage is applied is correct.

That being said the very first mission in Crusade has 2 rather large combats that is great for seeing how combat plays out. You can click on each ship to watch the values change in realtime. 

The one of the best ways to understand combat is to click on each ship and watch the combat log. Although my screenshot just s

>< - defender had a defense so the damage was done is the sqrt(attack), might be attack/2, against the defenders defense of the same type rounded down. So a missile attack of 5 will do 2 damage against its targets point defense.

>> - defender doesn't have any defense against that attack so full damage is applied to the hull. So 5 damage will be applied to the ships hp. If this leaves the ship <= 0 the ship is destroyed. I think the as long as you have at least 1 point of the given defense for a given attack you wont receive any hull damage. This is why you can sometimes see a lot of little ships with minimal defense take on a larger ship with big guns. 

Also in the UI it will highlight the attack and defense types used in the calculation.

So the TAS Megaera has 5 missile attack and the defender has 12 point defense. Both are yellow icons.

Attacker

dmg / 2 =2.23...

rounded down = 2

The defenders point defense is reduced by 2 

The manual is a great resource and goes into more depth like how the ships choose targets. I was amazed that after all the time I played I still learned something form the manual that I didnt understand before.