To elaborate on ConMan's answer, here is the direct text of the rules:
"+X Action(s)" – the player may play X number of additional Actions this turn. +X Action(s) adds to the number of Actions that can be played in the Action phase. It does not mean play another Action immediately. The instructions on the current Action card must be completed before playing any additional Actions."
As the bolded part indicates, +Actions are treated like a resource pool. You complete the card giving you +Actions, then you may play an additional action, completely resolving that card. You may continue playing actions until you run out of available actions in your "action resource pool" (which is not an official Dominion term, but is useful for explaining the mechanic).
So, in your case, you would resolve Village, which draws you one card and adds two actions to your "action pool." Then, since you have actions remaining, you can choose to play another action card from your hand, completely resolving it. This would be the Smithy in your example, so you would draw 3 cards. Then, you still have an action remaining in your "action pool," so you may choose another card from your hand. At this point, your hand includes the 3 cards that you drew with Smithy, so any of those cards are fair game.