I've been reviewing old family recipes, and I've seen pickled onions called for in some soup, stew, and casserole recipes as an accent; this may or may not be because my foremothers grew and canned loads of onions. It's worth an experiment or two, I think!
I own the same book and was similarly surprised when I read that instruction, but in the section on ingredients, the author does mention a particular variety of onions called pink onions. The mention is on pg. 32, and there is a picture of a pink onion on the upper left of pg. 34.
Here's an excerpt from pg. 32:
"The longer the onions are fried, the browner they will get and the deeper the color of the curry will be... When the onions are fried until only light pink in color, they will impart a sweetish taste to the curry. Certain varieties of onion, like Spanish onions, are too sweet to be appropriate for curry-making. The most appropriate from the taste point of view are the French and the small pink English."
From 50 great curries of india
I've never seen pink onions in any of the local markets (in northwestern US), I used white onions and sauteed them just to the point of browning. The recipe turned out fine, but it's a lot of onion. (The recipe calls for 2 large onions, finely chopped. It's a recipe that produces 2 servings.) Personally, I'd go a little lighter on the amount of onion or use yellow onions (despite the author's recommendation against Spanish onions), but that is just personal preference from a Western palate.
Note: it looks like the current printing of the book is different from the one I own, so the page numbers I cite may be off, but if you search inside the book (on Amazon) for "pink onion" you can see the page I've cited and the picture of what the author calls a pink onion.
Best Answer
First, finely chop the onions. This makes them smaller, faster-cooking, and less of a textural presence in the dish. Do it by cutting straight through the poles of the onion, resulting in two halves. Then chop off the knobs and peel off the outer layer. Run the knife 8 or 9 times along the vertical (from pole to pole), but don't sever one end completely. Cut finely across these verticals to make a fine dice. Run the knife over the pile a few times if your cut isn't small enough.
Second, cook the onions. The purpose of sweating is to draw moisture out, concentrating the flavor and enhancing conversion from starch to sugar. Heating the onions releases their aroma and reduces the chemical bitterness they exhibit when raw. Heat up some oil in a pan to medium-low heat. Add the onions. Add salt. I wouldn't cover the pan, since the lid will prevent steam from escaping. Stir/shake to prevent sticking or burning. The onions will get soft and then translucent. (Eventually, if you kept going they would get limp and browned; this is referred to as caramelized and considered a different thing than sweated, so although it's just further along the same spectrum, you shouldn't go that far for this recipe).
That's how I'd do it and why. I don't know if it's a textbook answer.