how do flip cards work in mtg

how do flip cards work in mtg double-sided Magic the Gathering gameplay? I've seen many cards like

Name: how do flip cards work in mtg double-sided Magic the Gathering gameplay? I've seen many cards like
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If you choose not to reveal or pay the alternate cost immediately, the card enters your hand and the miracle cost cant be invoked to cast the card later

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Mage Slayer Mage Slayer gives the equipped creature an ability I like to call first first strike. As in, it deals damage when you declare it as an attacker, before your opponent even gets to declare blockers