How does Jandor's Ring work with modern Magic rules?
Jandor Ring doesn't work under the current MtG rules. Luckily, it is too expensive in converted mana cost to see serious tournament play, but if it was your answer exists within the ruling you quoted. The current rules don't support a way of doing this, technically. (Edit: You added an additional question regarding which card could be discarded from a multi-card draw spell. If you examine the Oracle wording in the online Gatherer, you will note that you can only discard the last drawn card.)


  402.3. A player may arrange his or her hand in any convenient fashion and look at it as much as he or she wishes. A player can’t look at the cards in another player’s hand but may count those cards at any time.


Because the current rules don't support the card, because there is no easy way to achieve the desired behavior, the rulings tell you how to handle using the card.


  get a judge or put cards you draw aside until you decide whether or not to use this.


This is similar to the effect, but even more restrictive than a card like Sylvan Library (which has seen tournament play). With this card, you must keep cards you drew this turn separate from the cards that are in your hand if you intend on returning one of those cards this turn. (example: Brainstorm cast during your upkeep). The rules don't specifically tell you to keep your hand separate from the Brainstorm cards, but if you intend to return a Brainstorm card, you must keep them separate to preserve the game state.

You might be interested in this thread on the subject of cards currently not supported by the rules.