Well, this is just my understanding, so I might be completely off, but here goes. Most suppressors are designed similar to a muffler on a car. They have a series of baffles inside them that allow the hot, rapidly expanding gasses from the shot to expand relatively slowly and cool off a little bit at the same time. The noise that is associated with a rifle shot is only partly due to the actual explosion of the shot, the rest is the sound of the bullet breaking the sound barrier. When the gasses that are leaving the barrel and propelling the bullet are allowed to expand slowly and cool off the noise related to the shot is "suppressed" and therefore not as loud.
You can, and many people do, run a suppressor with normally loaded ammo just fine. There is still the sound of the round breaking the sound barrier, but the shot itself is generally quiet enough that you can shoot without ear protection and not suffer any hearing damage. I am not a SF/SWAT or anything like that, nor do I play one on TV, but from what I've heard suppressors are often used in situations where wearing ear pro might not be possible/practical but is still needed, such as on a raid or similar indoor scenario where you need to be totally aware of your surroundings.
Now, if you add subsonic ammo to the equation, you can have a rifle that shoots so quiet that all you hear is the bolt cycling and the impact of the round, more or less. The downside, as previously stated, is that to get a round to subsonic speeds you have to slow it down below 1100 FPS, which is a little more than a third of the muzzle velocity of a standard 5.56 round. This means that you lose a lot of the energy of the round, and for a 55 grain round it is velocity that makes it effective. Thus, it is really only practical to use subsonic 5.56 loads at close contact ranges. Of course, those are generally the scenarios where you would need subsonic and suppressed fire since, as previously stated, if you are engaging a target at range the round will get there before the sound will.
I have a friend who is a Class 3 dealer and manufacturer who has made a few different suppressors. One was for a .308 bolt gun for a guy who wanted to hunt hogs without his neighbors getting pissed at him all the time. He still used normal loads but they were much quieter with the suppressor and you can shoot the rifle without ear pro. I also got to shoot a little toy he made that I want badly just because it is so fun...a suppressed 10/22 which, when shooting subsonic ammo, is quieter than many pellet guns that I've shot.
Now, if you want one for your M&P you will need to fill out a BATFE Form 4, get fingerprinted, passport photos, have your local county chief LEO sign your Form 4, send all of the above in to the BATFE along with $200 for your tax stamp, and, assuming you pass the background check, you will receive your certified Form 4 and can now take your suppressor home with you. As to which suppressor to go with, I can't comment as I don't own one...yet...but there are a couple of options, again, as previously mentioned. You can get a thread-on suppressor that replaces your flash suppressor, or you can get a flash suppressor such as the Surefire 556 that is designed so that the Surefire suppressor slips over the flash suppressor and locks into place.
Anywho, I hope that some of that was helpful, and if I made any errors then those that are more knowledgeable feel free to correct me.