The reason I asked whether the person is a swimmer or not is because the experience and reactions are vastly different.
A non-swimmer will quietly sink until the nose is in the water, making upwards pushing motions with their hands that are below the water, and moving their feet in a sort of scissor kick. None of this will be very effective, but it is completely automatic. Even if the person is aware that they are drowning, they won't be able to raise their hand or otherwise indicate that they are drowning. Most non-swimmers, however, will not even be aware that they are drowning, as their mind goes onto auto-pilot. They frequently don't remember anything after being rescued.
Swimmers, however, have a skill set that enables them to use some level of logic. They will try concerted actions to breathe. Their minds will frequently be completely focused on those actions. Puma describes the feeling fairly well, as the mind becomes very goal oriented. As the person continues to struggle without success, a feeling of hopelessness begins to descend. At that point you can have flashbacks or remember your life. Once you kick into real panic, most people won't remember anything, other than a feeling of being overwhelmed and scared. Real panic makes you go on auto-pilot, destroying our ability to think in a higher fashion. Swimmers early in the process may wave their arms and/or call for help. As the process continues, they no longer have the energy for it.
I've pulled out enough people, but never felt the need to try it myself.
Best of luck,
Jim Clark-Dawe