The creature blocks only if it’s able to do so as the declare blockers step begins. If, at that time, the creature is tapped, it’s affected by a spell or ability that says it can’t block, or no creatures are attacking its controller or a planeswalker controlled by that player, then it doesn’t block. If there’s a cost associated with having the creature block, the player isn’t forced to pay that cost. If that cost isn’t paid, the creature won’t block.

The controller of the creature chooses which attacking creature that creature blocks.