Leyline of the Void affects cards that would be put into opponents’ graveyards from anywhere, not just from the battlefield.

Your “opening hand” is the hand of cards you decide to start the game with after taking any mulligans.

After all players have decided not to take any more mulligans, if the starting player has any Leylines in his or her hand, he or she may put any or all of them onto the battlefield. Then each other player in turn order may do the same.

Leylines that start the game on the battlefield aren’t cast as spells. They can’t be countered.

After each player has exercised his or her option to put Leylines onto the battlefield, the first turn of the game begins.

Leyline of the Void’s second ability prevents cards from ever reaching your opponents’ graveyards. Abilities that would trigger when those cards are put into an opponent’s graveyard (such as Hoarding Dragon’s last ability) won’t trigger.

Leyline of the Void’s second ability doesn’t affect token permanents that would be put into an opponent’s graveyard from the battlefield. They’ll be put into that graveyard as normal (causing any applicable triggered abilities to trigger), then they’ll cease to exist.

If your opponent discards a card while you control Leyline of the Void, abilities that function when that card is discarded (such as Liliana’s Caress’s ability, or a madness ability of the discarded card) still work, even though that card never reaches that player’s graveyard. In addition, spells or abilities that check the characteristics of the discarded card (such as Chandra Ablaze’s first ability) can find that card in exile.