You cast the card before shuffling your library (if it was searched). In some very rare cases, you may need to take actions involving your library while casting the card. For example, if it has an additional cost and you activate Deranged Assistant's ability ("{T}, Put the top card of your library into your graveyard: Add {C}.") to pay for it, you must maintain the order of your library while you search it.
If you cast a card "without paying its mana cost," you can't pay alternative costs such as overload costs. You can pay additional costs such as kicker costs. If the card has mandatory additional costs, you must pay those.
If Aether Searcher leaves the battlefield before its ability resolves, you'll still be able to search for the named card and cast it.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. James Paick
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
When casting a card this way, ignore timing restrictions based on the card's type. Other timing restrictions, such as "Cast [this spell] only during combat," must be followed.
If Aether Searcher is the last card you draft in any draft round other than the last one, you'll reveal the first card you draft in the following draft round and note its name.
If the card you draft after Aether Searcher is a land card, you won't be able to play that land using Aether Searcher's ability.
If the card has {X} in its mana cost, you must choose 0 as its value.
If an Aether Searcher owned by another player enters the battlefield under your control, you can search for a card you've named while drafting a card named Aether Searcher, not a card named by its owner. Unless you also drafted a card named Aether Searcher, you won't cast a card.
If Aether Searcher is the last card you draft, there won't be a noted name. You can still search your hand and/or library when it enters the battlefield, but you won't cast any card this way unless you also drafted an Aether Searcher and noted a card then.
