If you somehow manage to cast Enter the Unknown when it's not your turn, the target creature explores when it resolves, but you won't be able to play a land that turn.

If an ability instructs a creature to explore, its controller reveals the top card of their library. If it's a land card, they'll put it into their hand. Otherwise, they'll put a +1/+1 counter on that creature, then choose to either leave that card on top of their library or put it into their graveyard.

Once an ability that causes a creature to explore begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the exploring creature after you reveal a nonland card but before it receives a counter.

If a resolving spell or ability instructs a specific creature to explore but that creature has left the battlefield, the creature still explores. If you reveal a nonland card this way, you won't put a +1/+1 counter on anything, but you may put the revealed card into your graveyard. Effects that trigger "whenever a creature explores" trigger as appropriate.

Enter the Unknown's effect allows you to play an additional land during your main phase. Doing so follows the normal timing rules for playing lands.

If no card is revealed, most likely because that player's library is empty, the exploring creature receives a +1/+1 counter.

In some unusual cases, noncreature permanents may explore. For example, if the creature card returned by Defossilize is somehow not a creature once it's on the battlefield, it can still explore. You'll take all the same actions, and you may end up putting a +1/+1 counter on the permanent. (Note that some effects target a creature, and those effects would still require a legal target to have it explore.)

The effects of multiples of Enter the Unknown in the same turn are cumulative. They're also cumulative with other effects that let you play additional lands, such as the one from Wayward Swordtooth.

If the target creature is an illegal target by the time Enter the Unknown tries to resolve, the spell doesn't resolve. It won't explore, and you won't be able to play an additional land.

Some spells or abilities might cause a creature to explore multiple times in a row. If you reveal a nonland card when a creature explores and leave it on top of your library, then the creature explores again immediately afterwards, you'll reveal the same card again.