Quick answer
llevar = to take something away from here.
traer = to bring something towards here.
Side by side
Llevo el pastel a tu casa.I am taking the cake to your place.
Trae el pastel a mi casa.Bring the cake to my place.
Memory trick
Stand where you are speaking from. Movement away is llevar; movement towards you is traer.
Typical mistakes
¿Me llevas un café?
¿Me traes un café?
You want it to come to you.
Traigo a los niños al colegio.
Llevo a los niños al colegio.
The school is away from where you are.
Check yourself
Camarero, ¿me ___ la carta?