E.2.1- A 'cantrip' is a spell which has an effect and also lets you draw a card as part of the effect. This can be done as part of the resolution, or it may be done during the next turn. [CompRules 1999/04/23]
E.2.Ruling.1- If instructed to draw during the next turn, do so regardless of which player's turn that is. You'll often be drawing during your opponent's turn. [D'Angelo 1997/04/11]
E.2.Ruling.2- If the spell has a target and all of its targets are illegal on resolution, then you will not get to draw a card. See Rule G.39.6. [D'Angelo 1998/02/03]
E.2.Ruling.3- If the spell is countered, you do not get to draw a card. [Duelist Magazine #7, Page 8, 1995/10/01] See Rule G.7.2.
Note- Many of these cards received errata. It's best to check the card listing for details.