To "discard" a card, choose a card from your hand zone and put it into your cemetery. Some effects modify where the discarded card(s) come from. For example, an effect which tells you to discard your "top spell," means you discard the topmost card from your spellbook.
By default, you may choose which card to discard, though many effects will tell you to discard a random card, spell, or site.
Cards that are in zones other than a player's hand cannot be discarded, unless explicitly stated. For example, if you summon a , you cannot discard a card from 's hand to pay for its effect.