So, I beat up a group of kobolds or whatever and my fighter/cleric detects a magical item in the pile. It has an * in front of it so I assume that's what that means anyway. So I take it but... Now what? I have a leather armour with an asterix and I don't actually know what bonus it has. How do I tell? None of the manuals seem to have any illumination I can find on the matter...

You can ID them in shops and temples.

Before you get back to a shop you can also equip the item and see how it affects your character's AC (or THAC0/damage in the case of a magic weapon). Be careful with this technique though (save your game first) because if the item is a cursed magic item it will have a negative effect and you won't be able to unequip it! Also if you use this method you will have to remember that the item is actually magical, so it's best to ID them eventually as PetrusOctavianus said if it's an item you want to keep.