Here is how we made pomme puree at the restaurant I used to work at, for a very well known (in Canada anyway) French chef: Peel and boil as many potatoes as you need.
Cook until slightly underdone.
Run the potatoes through a ricer/food mill.
Then--this is key--scrape the result through a tami--a very fine mesh sieve.
Most often used for sifting flour.
Usually about 14-18" diameter, looks like a drum.
Return resulting potato to a pot, add melted butter, cream, salt, pepper, nutmeg to your desired consistency, stirring all the time.
If not serving immediately, chill as fast as possible, and reheat to order in a pan using a little more cream to loosen it up.
IMPORTANT: you must work as fast as possible; the potatoes need to stay hot the whole time or will become gluey.
cooking.stackexchange.com/users/None/
Here's how I make mine, which I like and got my wife eating mashed potatoes for the first time since childhood.
I steam the potatoes rather than boil them, which results in something that tastes more like potatoes than the boiling version and avoids the waterlogged problem that mis-timing the boiling can bring.
Peeled and cut into chunks, I steam until tender.
I either just use a masher and enjoy the few leftover chunks or I use a ricer to mash them into the large bowl.
Then I add just a bit of butter, a few dollops of fat-free sour cream and then start adding milk.
I keep adding milk and mixing by hand until they're creamy, which, based on what I've seen in other recipes, etc.
is quite a bit more milk than is typical.
They even reheat fairly well.
Of course, I could just be deluding myself and mine
are among the worst, most gluey around.
cooking.stackexchange.com/users/104/J Wynia
Many chefs swear by using a potato ricer instead of a mixer; it is said to be less likely to rupture the cell walls and produce glueyness.
I just bought one, so I'll let you know how it works.
cooking.stackexchange.com/users/1393/Michael Natkin
I find using Yukon gold potatoes work best, be sure to boil until tender all the way through.
Don't over beat with a mixer, use medium speed, and add softened butter.
Milk, cream, or sour cream will also increase the creaminess without making mashed potatoes sticky.
cooking.stackexchange.com/users/1769/Jenn
here's what I do, and I make mine different than most people here: Boil skin on when slightly over done run under cold water and deskin pan fry
the existing pealed potatoes season with salt pepper, and
whatever else you like ( i like cayenne and usually infused the oil with garlic
then take it out) when the potatoes are hot mash slightly and add a bit of cream stir like crazy (off heat)
add a bit of olive oil put back on heat repeat process until you got it silky enough for your liking
cooking.stackexchange.com/users/87/dassouki
The kosher version:I slice the potatoes as thinly as possible then add them to a pot with boiling water and a little salt.
When the water begins to boil, I cover the pot and lower the heat (to prevent the water from boiling over).
Then I slice, dice and fry an onion.
When the onion has reached a nice brown colour, I stop frying and put the onions (and any remaining oil) into a mixing dish.
I then take the potatoes off the heat and strain them, washing them to remove excess starch.
I add the potatoes to the mixing bowl, add two spoonfuls of mayonnaise (normally 5% fat) and about 1/4 cup olive oil.
Then I mash and mix.
On top of the potatoes I scatter paprika.
If it were up to me, I would also add some sliced parsley, but the family doesn't like that.
I prefer to put the mashed potatoes (uncovered) into the oven for about half an hour at 75 centigrade, which dries them out and then use the oven's grill for a further ten minutes.
cooking.stackexchange.com/users/3469/No'am Newman
I can't say this is the best way, but it is different...
I use a slow cooker to make supper, anyway, so I wrap some potatoes in aluminum foil and stick them on top of the chicken (or whatever)
that's in the stoneware.
When it's time to eat, I take the potatoes out, peel them, and mash with a fork into a bowl.
Then I stir in some hot water and a little salt, or some of the gravy from whatever was cooking in the crockpot.
It comes out really good, and it's very simple :)
I don't think it's gluey at all...
cooking.stackexchange.com/users/4198/chama
What are the key factors in making silky smooth (non gluey) mashed potatoes.   What technique has the best results?
How can I make a silky smooth, rich mash?
cooking.stackexchange.com
<potatoes><mash>
cooking.stackexchange.com/questions/4495
cooking.stackexchange.com/users/138/Sam Saffron
Choose suitable potatoes like Yukon Gold and cook until slightly underdone, but not hard in the middle. Steaming can prevent the potatoes from becoming waterlogged, and using a ricer rather than mixer makes rupturing the cell walls less likely. Boil or steam potatoes until slightly underdone. Run them through a ricer while they are still hot. Add milk or cream for extra creaminess.
Cook the potatoes either by boiling or steaming until slightly underdone. Yukon potatoes work well for mashing. Run the potatoes through a ricer. You must mash them while they are still hot to avoid them becoming gluey. Milk or cream will improve the creaminess.