Another thing I wish someone had told me when I first started cooking: you should cook potatoes in cold water. Obviously you do need to apply heat, otherwise you just get wet potatoes. The idea is to put them in a pan of cold water and then bring it up to the boil.
I think I learned this from a TV show where it was simply stated as Truth without explanation, but you can see why it makes sense: you don’t want the outside of the potato to be cooked while the middle is still raw. That’s not a problem with something like green beans, so those can be put straight into a pan of boiling water.
So for example, to make delicious boiled new potatoes: put the potatoes into a pan, add enough cold water to just cover them, and heat it until the water starts to boil. Add some salt, put a lid on the pan, and leave it on a low heat until the potatoes are cooked (test by sticking a knife into them). Drain the water off, chuck a bit of butter and some salt and pepper into the pan. Add some chopped chives or something, if you like. Swirl the potatoes around a bit to coat them with butter, take them off the heat and leave with the lid on for a few minutes so they absorb some of the butter and seasoning.
The potatoes will retain their heat for a surprisingly long time in a covered pan, so I often put the potatoes on the heat even before I’ve decided what else I’m cooking. They’ll still be fine after sitting around for twenty minutes or so.
The other cunning tip about boiling potatoes is: don’t just throw away the water you cooked them in. It serves as a sort of basic stock, just a bit more savoury than plain water. I always use it in the gravy when I’m cooking a roast, for example. I’m not suggesting you keep little tubs of it in the freezer; just don’t tip it straight down the sink, in case it comes in handy.