One way to do this is to stir in a gallon of ice water to the wort. The next step is to transfer the wort to the carboy. Add the rest of the water to the carboy. After the wort has been transferred to the carboy, the yeast is added to the wort. Be sure to add the yeast only after the wort has cooled down.
Yeast is a living organism.
If you put it in hot liquid, it will die. Put the fermentation lock in the top of the carboy. The wort will begin to develop a head of foam within 1 hour. The head of foam will get larger over the next 24 hours. After 24 hours the foam should subside.