Think in directions
Draw a dot for yourself. Traer is anything coming toward that dot; llevar is anything moving away from it. When you're on the phone and someone says ¿puedes traer pan?, they mean bring it here — to them. When they say ¿puedes llevar a los niños al colegio?, the school is the destination, not where the speaker is.
Llevar for duration
One of llevar's most useful constructions is llevar + time + gerund to express how long you've been doing something: Llevo dos horas esperando (I've been waiting for two hours). This construction has no equivalent with traer.
Wearing clothes
Use llevar (not traer, not ponerse) to describe what someone is wearing at a given moment: Lleva una camisa azul = He's wearing a blue shirt. Ponerse is the action of putting clothes on.