Prep time: 10 minutes Cook time: 25 minutes Yield: Serve 4

Ingredients:
1 1/2 - 2 lbs Starchy potatoes - (about 4) Russet or (about 5) Yukon Gold.
  Starchy potatoes will just fall apart after sufficient cooking.

1/2 teaspoon salt
4 Tbsp (1/4 cup) - 1 cup milk, heavy cream or buttermilk
2 Tbsp  butter
Optional:
2 whole garlic heads
chopped fresh basil or parsley
Shallots or chives
Rosemary
Saffron threads
Nutmeg
Sherry

NJ Governor Christie's recipe includes, Boiled and pureed rutabaga, butter, sour cream, cream cheese, Romano cheese, milk and heavy cream.

At Perfect Mashed Potatoes | SimpleRecipes.com Elise says,
"Everybody seems to have their favorite way of making mashed potatoes. Some cook them with the peel on, some without. Some add a little of the cooking water to the mashed potatoes for extra starch. I have found that the single thing that makes the biggest difference for making perfect creamy, heavenly potatoes is the type of potatoes you use.

Most people use starchy Russets for mashed potatoes. With their high starch and low water content, they're good for baking, for making French fries, and for mashing. Here's my secret though--even better than Russets for mashing are Yukon Golds. They're a little more expensive than Russets, but worth it. They're naturally creamy when mashed, never mealy, and have a slightly buttery flavor all on their own. Yukon golds make the most perfectly creamy, buttery mashed potatoes."

Some people like Small yellow, white or red potatoes for creamer mashed potatoes, others feel they come out too waxy.

Tools - Utensils: - Masher or Ricer (produces rice sized pieces of potato)
   
 

The Endurance Potato Ricer by RSVP International, came out tops at
Potato Ricers Review - America's Test Kitchen
They liked the ones without holes in the side.

A food mill will also work.
Or you can use a standard strainer and push the potatoes thru.
See also Tools for Mashing Potatoes | MathaStewart.com

Do it:

Peel the potatoes and cut into about 2 inch cubes.
Put the potatoes into a large pot, 2 tablespoons salt, and cover with cold water, about 1 in over the potatoes. Bring to a boil* over medium-high heat and cook until the potatoes are tender, about 20-25 minutes, until they are fork tender. Drain them well. Let them dry for a while.
* Note: Some say to simmer them not boil; that way they’ll stay intact and cook more evenly.

At SteamyKitchen they recommend steaming. The gentle treatment makes it less likely to get gummy, gluey and mealy mashed potatoes.
You can also bake them.

Optional:
Cook in some stock
Add a bay leaf

Jack Faherty, an executive at D'Artagnan Foods, says the secret is to get the potatoes really dry by putting them in the oven after cooking.

Garlic butter recipe at CookingLight (you can make this several days in advance)

Meanwhile, heat the cream and butter in a small saucepan.
Some say not to heat buttermilk, it will separate. Others say it will come back together in mixing.

Put the potatoes through a ricer or food mill into a bowl.
Stir in the milk mixture with a whisk or rubber spatula.
Use plenty of milk so they are almost soupy. Keep stirring the potatoes. They will absorb most of it.
(you can also add some stock here)
season with salt and pepper.
Mix together with a spoon, spatula or wisk and add the chives.

To keep the potatoes warm, place the bowl over a pan of simmering water for up to 30 minutes. You can add a little extra hot milk to keep them creamy.

Common Mistakes
Don't use a food processer, They come out like glue.
Don't overmix the potatoes; They'll get gluey!
Don't cut the potatoes too small; They'll absorb too much water.
Don't undercook. They should be ready to fall apart when done.
Don't use enough milk or cream.
Source: You're Doing It All Wrong - How to Make Mashed Potatoes - CHOW - YouTube
See also: 5 Common Mistakes to Avoid When Making Mashed Potatoes — Tips from The Kitchn | The Kitchn
and 9 Mashed Potato Mistakes - Bon Appetit

Experiment. You'll have fun.

Links:
The Best Recipe for Mashed Potatoes | Good Housekeeping
Buttermilk Mashed Potatoes | Food Network
Do-Ahead Mashed Potatoes | Betty Crocker