When do I discard a card for Skeleton Key?
You draw the card first. You can even discard the card that you drew. In general, you always follow instructions in the order written on the card.

Interestingly, this doesn't appear to be specified in the basic rulebook or quick start guide. But here's the rule from the comprehensive rules for it:


  608.2c The controller of the spell or ability follows its instructions in the order written. However, replacement effects may modify these actions [...]