I use Mudbug's method...
and yes, I lift the lid.
The formula that Mudbug posted is what I learned decades ago as the oriental way to cook rice (it was described in a Chinese cookbook of the time), and it's always worked well for me regardless of the amount. There are a couple of modifications that can be made to adjust for very large amounts or very small amounts.
The "water up to the first knuckle" measurement seems to work out to about 1 1/4 as much water as rice (a little more than that for small amounts). With very small amounts, which I usually do, just using 1 1/4 as much water works best for me.
The three levels of heat are needed for large amounts, but not smaller ones (less than about 1 1/2 cups raw rice). With the smaller amounts, you can just boil and then turn down to very low for 30 minutes.
This cooking method will leave a crust of rice on the bottom of the pan, which may be a little brown but should not be burned, and is served as part of some Chinese dishes. I avoid it by violating the DO NOT LIFT LID instruction just enough to stir the rice as I'm turning it down to very low. I've found that, unlike souffles or 19th century cake recipes, rice doesn't collapse if you lift the lid for a very short time, and mixing the rice up just before the long, slow simmer keeps the bottom from drying out and crusting over.
What that description doesn't call for is washing the rice before cooking. Oriental cooks would run cold water over the rice and stir, changing water until it doesn't cloud over. That washes loose starch off the rice (and probably a bunch of water-soluble vitamins), and gives it a slightly different consistency than just tossing into the pan with water and cooking (it seems a little less "gluey"). Either way comes out good.