Here is how to make mashed potatoes the improvisational way:
Peel (or don’t, especially if you are using red potatoes) and hack to bits some potatoes. Put them in a pot and cover them with cold, heavily salted water. Boil them (and give them a stir occasionally so they don’t stick and burn). You can skim off some of the potato starch, as it’s released and floats on the surface, with a large spoon; this reduces the odds that the water will climb up out of the pot and require your intervention.
When the potatoes are very soft (to check, grab a piece that’s above average in size with your spoon, run it under the faucet for a few seconds to cool it off, and eat it: it should barely require the possession of teeth), dump them out into a colander in the sink to drain off the water. Dump them back in the pot and start mashing them up – you can use a potato masher if you have one, but a big fork will do in a pinch. Thin the mixture to your preferred texture by stirring in splashes of milk or cream. Add salt to taste.
You can add Better Than Bouillon to the water in which you boil the potatoes, especially if you aren’t planning to add anything interesting to them later.
You can boil the potatoes with coarsely chopped garlic (it has to be big enough that you won’t lose it in the colander), onions, or other vegetables that will become mushy enough to mash. I don’t recommend adding herbs or spices at this stage because they’ll just go down the drain, but something like a bayleaf would work. (Remove the bayleaf before you start mashing the potatoes.)
In addition to the milk or cream you need to get the mashed potatoes soft and moist and goopy, you can add butter, oil, sour cream, soft cheese (I like Boursin, especially the Garlic and Herb kind), or, again, Better than Bouillon. Sour cream has a soft enough texture (compared to most cheeses), and tastes good enough even in large quantities (as opposed to butter or oil) that if you plan to use a lot of it, you may be able to dispense with the milk or cream. I recommend adding these items before the milk or cream in any case, because they do affect the texture.
In addition to the salt all mashed potatoes demand, you can add other herbs and spices. White pepper, tarragon, chives, garlic powder, onion powder, dill, ground celery seed, ground mustard seed, and sage are nice in mashed potatoes, although perhaps not all at the same time.
Whatever you add to your potatoes, taste them between each addition to make sure you’re on the right track.
The people who make Boursin are not paying me either. In fact, nobody involved with any kind of food is paying me, so I’m going to stop issuing disclaimers now.