During his turn, the player may play any number of cards he wants, with some limitations. Players are not forced to play cards during the second phase.
Brown-bordered cards are played by putting them directly into the discard pile and applying the effect described with text or symbols on the cards.
The Beer and Missed! cards are the only cards players may play outside of their turn.
Blue-bordered cards are played face up in front of you (exception: Jail). Blue cards in front of you are hence defined to be 'in play'. The effect of these cards persists until they are discarded or removed somehow.
Players can have as many blue cards in front of them as they want, providing they follow the limitation rules.