Text (LG+errata): Starting with you, each player may put a permanent card from his or her hand onto the battlefield. Repeat this process until no one puts a card onto the battlefield. [Oracle 2009/07/08]
The cards put into play during Eureka enter play one at a time. [Aahz 1994/06/22]
The cards are put into play and will not trigger effects which trigger on such cards being "played". [D'Angelo 2000/04/09]
Any abilities that trigger due to these cards coming into play do not actually resolve until after the entire Eureka effect is done resolving. [WotC Rules Team 1998/02/01]
Continuous effects of cards put into play take effect immediately. [Aahz 1995/12/18] For example, Kismet.
Each player gets a chance to put a card in play starting with you and going around the table to the left (unless your multiplayer variant defines a different ordering). A player may decline to put a card into play when it is their turn. The spell ends when all players decline in a row. [D'Angelo 2002/01/10]
If the card has an X in its mana cost, treat X as zero. [D'Angelo 2002/03/16]
Extended tournaments (see Rule 913) have always banned this card.