VP cards stay in your hand until the end of the game when playing Basegame or Seafarers expansion.
Once you draw a VP card the VP will get added to their overall score automatically. Please note that only you will be able to see your total VP score. Another Catanian playing with you won´t see that the VP from the VP card was added to your overall VP count.
In Cities&Knights/Special Scenario games VP cards get played automatically. It won´t remain in our hands the VP will get added for everyone to see to your total VP count.