Permanents you control have ward {2}. At the beginning of your end step, mill two cards, then exile a nonland card at random from your graveyard. Copy it. You may cast the copy without paying its mana cost.
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If the copy has {X} in its mana cost, you must choose 0 as the value of X.
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If you cast a spell "without paying its mana cost," you can't pay any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.
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If you don't cast the copy (perhaps because there are no legal targets available or you don't want to), the copy will cease to exist.
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The card remains exiled no matter what happens to the copy.