I keep hearing about adding some of the pasta water to the sauce, either to thicken it or to make the sauce stick to the noodles. But when are you supposed to do this? Wouldn't you be boiling your noodles right before you eat them? And wouldn't the sauce be finished cooking at that point? Wouldn't adding water then just dilute your wonderful tomato sauce?
This is a technique used for sauces that are otherwise very thick, such as a well-reduced marinara or a cream sauce (which will thicken as it cools). You wouldn't add it to a sauce which is already at the right texture.
As you deduce, yes, it's the kind of thing you do just before serving. You boil the pasta, save some of the water, and stir it into the sauce. You might give it another minute of cooking to ensure that everything is well incorporated, then plate the dish. The starch in the water gives it a supple texture that simply thinning with plain water wouldn't achieve.
This is an old restaurant trick, and they do it a little differently. They'll end up using the same water over and over, maybe for the entire service, so it's very starchy and thick. Doing it at home is a little different, since you won't have as much starch, but it's still a ready source of hot water that can be used to perfect the texture of a thick sauce.
Cream sauces like alfredo are especially useful for this: the starch water doesn't change texture as much as the cream does during cooling, so the dish stays at the right level of thickness as the diner eats. This may not be quite as necessary at home, where it isn't necessarily part of a long dinner service (and where the dish won't ever have to wait at the pass for other dishes to finish). Still, it's a good tool to have in your toolbox.
So, if you've got a perfect tomato sauce, don't do anything to it except eat it. But if you've been cooking it all day, and you find it's more "ragu" than "sauce", the starchy pasta water is the right tool, right there.
I posted a link to a pasta water blind test article on another question today, and will also post it here: This is Serious Eats' pasta water test. Beside the "how much does it thicken" test, the author also made a taste test with and without pasta water.
The pasta that had been cooked in its sauce with some of that pasta water won by a landslide
In all fairness, he does not compare it to other pasta-water-adding methods, he compares it to 1) sauce without water added to the cooked noodles, and 2) noodles (finish-) cooked in the sauce, but without adding the pasta water. So it does not have to be the best method to add pasta water. But it is certainly a method which functions and enjoyed success among the eaters.