Mashed potatoes are a staple of the American diet. I love them. I am going to give you two ways to cook them, one takes very little prep time, the other takes more prep time, but is a better result, in my opinion.
In each case, the potato you use is the most important choice. For mashed potatoes you need a dry starchy potato, NOT a smooth waxy potato. So Russets, any kind of baking potato, even the common "white" potatoes all work well. Yukon Golds make for a good mash. Avoid fingerlings, reds, purples, young or new potatoes. They will be more waxy/sugary than starchy and will come out gummy.
The method of mashing is a topic unto itself. By hand works best, assuming you have a potato masher. You can also mash them by putting all of the ingredients in the bowl of your stand mixer and mash on a lower speed just until they are mashed and fluffy. I like my potatoes lumpy, but some people must have them smooth. In that case your mixer is pretty much your only choice. But be careful. It is easy to mash too much with a machine and turn the potatoes gummy. And from that you should know that you must never, ever, never use your food processor...unless you are making potato glue.
Cut the potatoes into chunks about the same size. I usually quarter them. If you cut them smaller, they cook sooner, but then you might as well do the better recipe below. In a pot cover with salted water and bring to a boil. Lower the heat and simmer for 20-25 minutes until tender (I see if I can poke a fork through them). Drain the water and put the potatoes back in the pot over low heat to dry them off a bit. Take off the heat and add the butter, 1/2 of the evaporated milk and a bit of salt and pepper. Mash. (see note above) Add evaporated milk as needed to get the consistency you want. Taste and adjust seasoning.
Melt 1/2 the butter on low in a dutch oven or other heavy pan that has a lid. If you are doing the garlic mashed potatoes, add the garlic to the melted butter and simmer for 3-4 minutes until golden, but not browning. Do not burn the garlic by turning up the heat. Low and slow. Add the potatoes, salt, pepper, all of the water and 3/4 of the 1/2 and 1/2. Turn up the heat to medium until the liquid simmers, then turn the heat to low and cover the pot, leaving it simmering for 20-25 minutes. The potatoes are done when they are completely tender, but not mushy. Turn off the heat. Add the rest of the butter. Mash (see note above) adding 1/2 and 1/2 as needed to get the consistency you want.