What does discard placebo tabs mean on my birth control? skip the pills and wait a week for a period or just start the new pack right away ?or both?

Could be both...: With great freedom comes great responsibility. A woman is free to choose whether or not she wants to have a period (called a withdrawal period). Her responsibility is to talk with her doctor and remember what was said. If the plan was to skip the period, then she skips the placebos and starts the next pack right away. If she wants a period, she waits usually a week before starting the next pack.