The Draw Phase occurs first in the round sequence of scenarios.
Any effects that occur at the start of the round occur now. Then, play proceeds to drawing cards.
In each other round, each entity that can draw cards simultaneously draws 1 card. Various effects may modify the number of cards drawn. Entities with no cards left to draw should instead shuffle their discard pile back into their deck instead of drawing a card. If they were to draw multiple cards, they may then continue to draw, but the shuffling counts as one draw.
For more information, see Player's Guide Chapter 3: Scenarios.