The player’s hand is made up of a maximum of seven cards, so if you have seven cards already, you cannot draw any additional cards.
At the beginning of the game, the hand consists of 6 cards drawn respectively from each deck for each player.

By default, players can not view opponent's hand, but some cards allow this (see Tracking Gear, Reconnaissance, Wulven Scout…).
Note that viewing opponent's hand can only happen during your turn, and when the opponent's turn begins, all his card is hidden, and you can not see the card the opponent draws and the one he sacrifices.

From hand, players can sacrifice, summon and discard cards.