First, the basics.
I like to use one potato per person I’m serving, plus one or two more on top of that, just to be sure. The brown-skinned varieties serve better here than the red-skinned ones, but if red is what you got, they’ll do fine.
Peel them, cut them up and drop them into a pot of boiling water. How long is going to depend on how big or small the chunks are, but when you can poke a fork into them without any resistance, they’re done. A slight drizzle of olive oil over the top helps keep the pot from boiling over.
Drain them, sprinkle in some salt and go to town with a potato masher. For standard mashed potatoes, you want to add a splash of milk and some butter as you mash them.
You don’t want to make standard mashed potatoes, though. You want to make fancy-pants mashed potatoes, so pick whichever of the approaches below best fits with your tastes.
Truffled: Use truffle salt instead of regular salt. A drizzle of black truffle oil wouldn’t hurt, either.
Cheesey: Grate in a hunk of Parmesan or Asiago before mashing.
Gorgonzola: Before pouring in the splash of milk, heat it on the stove and melt some crumbled-up Gorgonzola or other stinky blue cheese into it. (Why is this separate from “Cheesey?” Because Gorgonzola is awesome, that’s why!)
Bacon: Cook a strip of bacon (pancetta, the Italian bacon, works exceptionally well for this for some reason) per potato or two. Chop up the bacon and mash into the potatoes along with the bacon drippings.
Caramelized onion: Read this post.
Roasted garlic: Take two heads of garlic and break up the cloves. Place them on a doubled-over sheet of aluminum foil and drizzle with olive oil, wrap up in the foil and cook in a 350 oven for 30 minutes. You should be able to pop them right out of the skins, though you may want to let them cool for a minute or two. Then mash an appropriate-looking number into the potatoes. Save remaining cloves for midnight snacks
There is no reason you cannot combine any, or even all of these -- I once did cheesey roast garlic pancetta mashed potatoes -- though it will start to feel excessive at some point.