There are many ways to make basic mashed potatoes, depending on personal preference. For potatoes to mash nicely, you need to add an oil, such as butter, and a liquid, such as milk. For healthy alternatives and just as much flavor, use margarine and broth. A stand mixer makes the creamiest mashed potatoes, but the traditional potato masher does the trick as well.
Wash the potatoes with a vegetable brush and water.
Peel the potatoes or leave them with the peels on. The peels contain extra vitamins and fiber, but leaving them on will give you a less creamy mash.
Cut the potatoes in half if they are small, and in quarters if they are large. Don't cut them down any further than that unless you like watery mashed potatoes.
Have a large saucepan or pot (5 qt or so) ready with some water in it, and put the potatoes in the water as soon as they are cut to prevent browning. Add more water to completely submerge the potatoes.
Put the pot on the burner on high without the lid on. Once it reaches a rolling boil, turn it down to medium. Simmer for 20 minutes. Get an empty colander ready in the sink.
After 20 minutes, stab a few of the larger pieces with a fork. Are they soft all the way through, or is it hard to pull the fork out? If they are still hard, give them more time. If they are soft, take the pot off the stove and strain the potatoes in the colander. Lift the colander and give it a good shake to get out more of the liquid.
Put the potatoes back in the pan and back on the stove over medium-high heat. Set your timer for 1 minute and stir the potatoes constantly. This step further allows the potatoes to dry so your mashed potatoes won't be watery. When the timer goes off, put your potatoes in your stand mixer's bowl, or keep them in the pot if you will be using a masher.
Add 1 to 4 tbsp. butter or butter substitute. Let the butter melt in the hot potatoes while you get a measuring cup and measure 1 cup of milk or broth; microwave the milk or broth for 1 minute. The milk should be hot but not boiling. To save on time, you can add the liquid cold. Add 1/4 to 1/2 cup liquid to the potatoes.
If using a mixer, turn on your mixer at low speed and mix the potatoes. Check the consistency and add more liquid if it looks too dry. Add salt and pepper to taste. Add about 2 tbsp. of sour cream (optional, but it gives an extra creaminess that mashed potatoes often sorely need). Mix or mash the potatoes at a slightly faster speed until smooth. Scrape down the sides.
The choice of potato is key. Yukon Gold potatoes have a buttery flavor to start with, so you won't have to add as much actual bad-for-you butter and salt.
Under no circumstances should you use a food processor. It does horrible things to the gluten content of the potatoes and you will end up with a gooey mass.