It's even easier now, it would be easy for a 12 year old to understand which I guess is what they want.
Destiny Knot passes 5 random IVs down from the parents.
Everstone passes down nature of the pokemon holding it.
Females can pass their hidden ability. Males can pass their hidden ability ONLY when breeding with Ditto.
The baby will always be in the ball the female is in. Males cannot pass their ball even when breeding with Ditto.
Power items pass a specific IV from the held parent but do not stack with the 5IVs from destiny knot.
There are 2 day cares, 1 west of Mauville and 1 in the Battle Resort (postgame only).
Both males and females can pass egg moves. For a list if passable egg moves just check the bulbapedia page for that pokemon.
If you walk up to the day care kid in the battle resort from the bottom, get on your bike and hold left, then when you hit the water hold up, you can create an infinite loop to hatch eggs.
If a pokemon with the ability Flame Body is in the front of your party eggs will hatch faster.
That's all I can think off of the top of my head. Good luck OP.